The boyhood Newcastle supporter made the move to St. James' Park on deadline day.
Albion boss Potter said of the move: "We were not actively looking to sell Dan during this window but the transfer represents a very good transfer for our club and the player.
"Newcastle are Dan's boyhood club, and this move allows him to potentially play out the rest of his career at his home club.
"Ever since I have been at the club, Dan has been brilliant for me. He is a superb professional, adaptable and a great character on and off the pitch.
"We will miss him here, but we understand his reasons for wanting to move and he goes with our thanks and very best wishes for the future."