The 27-year-old has agreed a three-year contract and becomes Owen Coyle's fifth signing as Wigan manager.
Carson will compete with Ali Al-Habsi for a starting role now that Joel Robles has returned to Atletico Madrid, although Al-Habsi is currently recovering from shoulder surgery.
"I'm over the moon to join the club," said Carson, who spent two years in Turkey after moving from West Brom.
"Now the focus is to get my head down and start working hard in time for the new season.
"Coming into a squad with a new look to it is exciting. There are plenty of players coming in at the moment, but there are also a number of guys here who have been at the club for a long time.
"Everyone talks about how tough the Championship is and they're right, you have to be at your best if you're going to come out on top.
"With a lot of games to play it's going to be really demanding on us this year."