The 25-year-old embarks on a fresh start abroad after a difficult season in which he lost his place to Boaz Myhill before winning it back late in the campaign.
Carson spent three seasons with West Brom after joining from Liverpool, where he had been a frustrated reserve.
Turkish delight: Scott Carson has completed his move to Bursaspor
Albion manager Roy Hodgson said: 'In the three months I worked with Scott I cannot fault his professionalism and dedication.
'He has been a good servant to the club and I would like to wish him all the best for the future as he looks to broaden his experience by playing in a foreign country.'
Carson made his name as a teenager, excelling at Leeds after replacing another England goalkeeper, Paul Robinson.
But a move to Liverpool only led to frustration on the bench and he joined West Brom in the summer of 2008.
He suffered relegation with the Baggies but stuck with them and helped them bounce straight back, before being made club captain after the departure of Jonathan Greening.
Fresh start: Carson spent three seasons at West Brom but has opted to ply his trade abroad
In total he made 118 appearances for the club and sporting and technical director Dan Ashworth said: 'I would like to thank Scott for his efforts and contribution to the last three seasons.
'After the disappointment of being relegated from the Barclays Premier League he played a significant part in our last two successful seasons.
'It is a good opportunity for Scott to go to Turkey and on behalf of everyone at the football club I would like to wish him well in his future career.'
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Explore more:People: Paul Robinson, Roy Hodgson, Jonathan Greening Places: Liverpool, Leeds, United Kingdom, Turkey