BuddyPress Profile Data Moderator plugin allows site admins to enable/disable user notification on approval.

Here is a screenshot showing rge user profile approval notification settings:-

• Notify User On Approval:- If enabled, the user will be notified when the site admin approves their updated profile data.
• Approval Email Subject:- Subject for the email notification received by the user.
• Approval Email Body:- Content for the email notification received by the user.

Next: Configuring profile data rejection email notification for the user 

Previous: How to configure admin email notifications in BuddyPress Profile Data Moderator