diff --git a/static/js/settings.js b/static/js/settings.js
index 6c2133a362..fbbf5c9b0e 100644
--- a/static/js/settings.js
+++ b/static/js/settings.js
@@ -30,6 +30,7 @@ function setup_settings_label() {
         enable_login_emails: i18n.t("Send email notifications for new logins to my account"),
         message_content_in_email_notifications: i18n.t("Include message content in missed message emails"),
         realm_name_in_notifications: i18n.t("Include organization name in subject of missed message emails"),
+        presence_enabled: i18n.t("Display my availability to other users when online"),
 
         // display settings
         dense_mode: i18n.t("Dense mode"),
diff --git a/static/js/settings_config.js b/static/js/settings_config.js
index aa81d7d9c3..0bd9c4c6b4 100644
--- a/static/js/settings_config.js
+++ b/static/js/settings_config.js
@@ -216,10 +216,15 @@ const email_notification_settings = [
     "realm_name_in_notifications",
 ];
 
+const presence_notification_settings = [
+    "presence_enabled",
+];
+
 const other_notification_settings = desktop_notification_settings.concat(
     ["desktop_icon_count_display"],
     mobile_notification_settings,
     email_notification_settings,
+    presence_notification_settings,
     ["notification_sound"]
 );
 
@@ -245,6 +250,7 @@ exports.all_notifications = () => ({
         desktop_notification_settings: desktop_notification_settings,
         mobile_notification_settings: mobile_notification_settings,
         email_notification_settings: email_notification_settings,
+        presence_notification_settings: presence_notification_settings,
     },
     show_push_notifications_tooltip: {
         push_notifications: !page_params.realm_push_notifications_enabled,
diff --git a/static/templates/settings/notification_settings.hbs b/static/templates/settings/notification_settings.hbs
index e8837a98e2..910e094cf3 100644
--- a/static/templates/settings/notification_settings.hbs
+++ b/static/templates/settings/notification_settings.hbs
@@ -107,6 +107,15 @@
               label=(lookup ../settings_label this)}}
             {{/each}}
 
+            <h5>{{t "Presence" }}</h5>
+
+            {{#each notification_settings.presence_notification_settings}}
+            {{> settings_checkbox
+              setting_name=this
+              is_checked=(lookup ../page_params this)
+              label=(lookup ../settings_label this)}}
+            {{/each}}
+
         </div>
     </form>
 </div>
diff --git a/templates/zerver/api/changelog.md b/templates/zerver/api/changelog.md
index 69d0393370..fd3a989d61 100644
--- a/templates/zerver/api/changelog.md
+++ b/templates/zerver/api/changelog.md
@@ -15,6 +15,8 @@ below features are supported.
 * `zulip_version` and `zulip_feature_level` are always returned
   in `POST /register`; previously they were only returned if `event_types`
   included `zulip_version`.
+* Added new `presence_enabled` user notification setting; previously
+  [presence](/help/status-and-availability) was always enabled.
 
 **Feature level 2**:
 
diff --git a/templates/zerver/help/status-and-availability.md b/templates/zerver/help/status-and-availability.md
index b9f6b9ae6b..5fd561273d 100644
--- a/templates/zerver/help/status-and-availability.md
+++ b/templates/zerver/help/status-and-availability.md
@@ -33,17 +33,18 @@ they haven't set a status, no status will appear.
 
 There are four possible availabilities:
 
-* **Active** (<span class="indicator green solid"></span>): Zulip is open and in
-  focus on web, desktop or mobile, or was in the last 140 seconds.
+* **Active** (<span class="indicator green solid"></span>): Zulip is
+  open and in focus on web, desktop or mobile, or was in the last 140
+  seconds.
 
-* **Idle** (<span class="indicator orange"></span>): Zulip is open on your
-  computer (either desktop or web), but you are not active.
+* **Idle** (<span class="indicator orange"></span>): Zulip is open on
+  your computer (either desktop or web), but you are not active.
 
-* **Offline** (<span class="indicator grey"></span>): Zulip is not open on
-  your computer.
+* **Offline** (<span class="indicator grey"></span>): Zulip is not
+  open on your computer.
 
-* **Unavailable** (<span class="indicator grey-line"></span>): You can always
-  manually set your availability to unavailable.
+* **Unavailable** (<span class="indicator grey-line"></span>): You can
+  always manually set your availability to unavailable.
 
 For [Group PMs](/help/private-messages), a green circle
 (<span class="indicator green solid"></span>)
@@ -52,8 +53,9 @@ class="indicator green"></span>) means that some are active and some are
 not. A white circle (<span class="indicator grey"></span>) means that none
 are active.
 
-You can see when someone was last active by hovering over their name in the
-left or right sidebar.
+You can see when someone was last recorded as active by hovering over
+their name in the left or right sidebar (even if the user is marked as
+unavailable).
 
 ## Set yourself as unavailable
 
@@ -67,4 +69,25 @@ left or right sidebar.
 
 {end_tabs}
 
-This will also obscure whether you were recently active.
+## Disable updating availability
+
+Zulip supports the privacy option of never updating the availability
+information for your account.  The result is that you will always
+appear to other users as **Offline** (or **Unavailable**, if you've
+set an appropriate status), regardless of your activity in Zulip.
+
+With this setting, your "Last active" time displayed to other users in
+the UI will be frozen as the time you enabled this setting.
+
+{start_tabs}
+
+{settings_tab|notifications}
+
+1. Under **Other notification settings**, in the **Presence**
+   subsection, toggle **Display my availability to other users**.
+
+{end_tabs}
+
+Note that because this setting works by making your availability to
+updating, you'll still appear to other users as active for a few
+minutes after disabling updates to your availability.
diff --git a/version.py b/version.py
index d785789755..fca77a4e64 100644
--- a/version.py
+++ b/version.py
@@ -29,7 +29,7 @@ DESKTOP_WARNING_VERSION = "5.0.0"
 #
 # Changes should be accompanied by documentation explaining what the
 # new level means in templates/zerver/api/changelog.md.
-API_FEATURE_LEVEL = 2
+API_FEATURE_LEVEL = 3
 
 # Bump the minor PROVISION_VERSION to indicate that folks should provision
 # only when going from an old version of the code to a newer version. Bump
diff --git a/zerver/migrations/0280_userprofile_presence_enabled.py b/zerver/migrations/0280_userprofile_presence_enabled.py
new file mode 100644
index 0000000000..2943ef785c
--- /dev/null
+++ b/zerver/migrations/0280_userprofile_presence_enabled.py
@@ -0,0 +1,18 @@
+# Generated by Django 2.2.12 on 2020-05-01 16:22
+
+from django.db import migrations, models
+
+
+class Migration(migrations.Migration):
+
+    dependencies = [
+        ('zerver', '0279_message_recipient_subject_indexes'),
+    ]
+
+    operations = [
+        migrations.AddField(
+            model_name='userprofile',
+            name='presence_enabled',
+            field=models.BooleanField(default=True),
+        ),
+    ]
diff --git a/zerver/models.py b/zerver/models.py
index 24376f00c8..bb6caf7c76 100644
--- a/zerver/models.py
+++ b/zerver/models.py
@@ -916,6 +916,7 @@ class UserProfile(AbstractBaseUser, PermissionsMixin):
     enable_digest_emails: bool = models.BooleanField(default=True)
     enable_login_emails: bool = models.BooleanField(default=True)
     realm_name_in_notifications: bool = models.BooleanField(default=False)
+    presence_enabled: bool = models.BooleanField(default=True)
 
     # Used for rate-limiting certain automated messages generated by bots
     last_reminder: Optional[datetime.datetime] = models.DateTimeField(default=None, null=True)
@@ -1048,6 +1049,7 @@ class UserProfile(AbstractBaseUser, PermissionsMixin):
         pm_content_in_desktop_notifications=bool,
         desktop_icon_count_display=int,
         realm_name_in_notifications=bool,
+        presence_enabled=bool,
     )
 
     class Meta:
diff --git a/zerver/openapi/zulip.yaml b/zerver/openapi/zulip.yaml
index 495a87fb6a..142a77ee95 100644
--- a/zerver/openapi/zulip.yaml
+++ b/zerver/openapi/zulip.yaml
@@ -2897,6 +2897,13 @@ paths:
         schema:
           type: boolean
         example: true
+      - name: presence_enabled
+        in: query
+        description: |
+            Display the presence status to other users when online.
+        schema:
+            type: boolean
+        example: true
       responses:
         '200':
           description: Success.
diff --git a/zerver/tests/test_home.py b/zerver/tests/test_home.py
index be34f86ea0..d385da18bc 100644
--- a/zerver/tests/test_home.py
+++ b/zerver/tests/test_home.py
@@ -119,6 +119,7 @@ class HomeTest(ZulipTestCase):
             "pm_content_in_desktop_notifications",
             "pointer",
             "poll_timeout",
+            "presence_enabled",
             "presences",
             "prompt_for_invites",
             "queue_id",
diff --git a/zerver/tests/test_presence.py b/zerver/tests/test_presence.py
index 911570b5cd..ab31c6c2bd 100644
--- a/zerver/tests/test_presence.py
+++ b/zerver/tests/test_presence.py
@@ -605,3 +605,33 @@ class GetRealmStatusesTest(ZulipTestCase):
         self.assert_json_success(result)
         json = result.json()
         self.assertEqual(set(json['presences'].keys()), {hamlet.email, othello.email})
+
+    def test_presence_disabled(self) -> None:
+        # Disable presence status and test whether the presence
+        # is reported or not.
+        othello = self.example_user("othello")
+        hamlet = self.example_user("hamlet")
+        othello.presence_enabled = False
+        hamlet.presence_enabled = True
+        othello.save(update_fields=['presence_enabled'])
+        hamlet.save(update_fields=['presence_enabled'])
+
+        result = self.api_post(othello, "/api/v1/users/me/presence",
+                               dict(status='active'),
+                               HTTP_USER_AGENT="ZulipAndroid/1.0")
+
+        result = self.api_post(hamlet, "/api/v1/users/me/presence",
+                               dict(status='idle'),
+                               HTTP_USER_AGENT="ZulipDesktop/1.0")
+        self.assert_json_success(result)
+        json = result.json()
+
+        # Othello's presence status is disabled so it won't be reported.
+        self.assertEqual(set(json['presences'].keys()), {hamlet.email})
+
+        result = self.api_post(hamlet, "/api/v1/users/me/presence",
+                               dict(status='active', slim_presence='true'),
+                               HTTP_USER_AGENT="ZulipDesktop/1.0")
+        self.assert_json_success(result)
+        json = result.json()
+        self.assertEqual(set(json['presences'].keys()), {str(hamlet.id)})
diff --git a/zerver/views/presence.py b/zerver/views/presence.py
index 16b423fd3a..d841e75d9e 100644
--- a/zerver/views/presence.py
+++ b/zerver/views/presence.py
@@ -85,7 +85,7 @@ def update_active_status_backend(request: HttpRequest, user_profile: UserProfile
     status_val = UserPresence.status_from_string(status)
     if status_val is None:
         raise JsonableError(_("Invalid status: %s") % (status,))
-    else:
+    elif user_profile.presence_enabled:
         update_user_presence(user_profile, request.client, timezone_now(),
                              status_val, new_user_input)
 
diff --git a/zerver/views/user_settings.py b/zerver/views/user_settings.py
index a24967ed44..60ceed8010 100644
--- a/zerver/views/user_settings.py
+++ b/zerver/views/user_settings.py
@@ -200,7 +200,8 @@ def json_change_notify_settings(
         message_content_in_email_notifications: Optional[bool]=REQ(validator=check_bool, default=None),
         pm_content_in_desktop_notifications: Optional[bool]=REQ(validator=check_bool, default=None),
         desktop_icon_count_display: Optional[int]=REQ(validator=check_int, default=None),
-        realm_name_in_notifications: Optional[bool]=REQ(validator=check_bool, default=None)
+        realm_name_in_notifications: Optional[bool]=REQ(validator=check_bool, default=None),
+        presence_enabled: Optional[bool]=REQ(validator=check_bool, default=None),
 ) -> HttpResponse:
     result = {}