The 25-year-old, who was released by City this summer, has generally played at left-back during his time at Eastlands and will provide competition for Jon Harley at Turf Moor.
Boss Steve Cotterill said: "We are delighted to have Stephen on board. He was one of the first players that I spoke to in the summer and it has taken a long time to land him due to there being a fair bit of interest from the Premiership.
"But I think obviously with coming towards the start of the season, Stephen decided he did not want to wait around any longer and has decided to come to Burnley.
"He will give us good competition and extra defensive cover."