The 23-year-old centre-back arrives with extensive Championship and League One experience after loan spells at Swansea City, Stevenage, Hull City and Reading.
Burns joined City’s academy from Southend United at 13 and progressed through the ranks, winning the FA Youth Cup and Premier League 2 title.
He made his senior debut under Pep Guardiola in 2021, featuring in a 6-1 Carabao Cup win over Wycombe.
"I'm delighted to be here, and it's amazing to get the deal done. It's something we've been working on for a little while, having spoken to the Gaffer a few times, so it's nice to finally have it done,” Burns told Wigan website.
"After those conversations, it was a project I could see myself involved in, but I see this as a massive club. When I was growing up as a kid, I knew them in the Premier League, so that was big as well.
"The Gaffer stressed the playing style and how he works, and we have a similar view of how we should play."