The 27-year-old, whose arrival was announced on the Championship club's website is the fifth signing in a week by new manager Owen Coyle.
"Coming into a squad with a new look to it is exciting," said Carson who spent two years in Turkey.
"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 so I'm sure they'll help lads like myself settle in.
"Right now I can't wait to start getting involved."
No financial details were announced but media reports put the value of the deal at around £500,000.
Carson has not played for England since November 2011. He has been signed after first-choice Latics keeper Ali Al-Habsi was ruled out for several months with a hip injury.
Last season Bursaspor finished fourth and qualified for the 2013-14 Europa League.
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