By default, when you accept a friend request, or someone accepts your friend request, a “story” is published to your wall.
To stop this, you can edit your privacy settings.
1)
First, hover over settings, in the top right menu (next to the search box)
Click “Privacy Settings”
2)
On the Privacy Settings page, click
“News Feed and Wall”
3)
On the News Feed and Wall settings, simply un-tick the Add a Friend icon towards the bottom.
Click save changes.