Ingham, 24, has agreed a two-year deal and told Sunderland's official website: "There were four or five clubs interested, some of them big clubs, but I wanted first-team football.
"I was impressed with what Denis Smith had to say."
Ingham, of course, knows Denis well from his time on loan at Wrexham at the end of the 2003/04 season.
"Wrexham is a good club and I see it as a good chance to play and develop my career. We want to go up next season," said the Northern Ireland international.