The deal was finally completed earlier and he will go straight into the team to face Norwich tomorrow.
Wright has been involved in all of City's first team pre-season matches after being released by Sunderland and has impressed those who watched him and the City staff who were delighted to sign the former Liverpool,Crewe and Stoke man.
"It seems like it's been quite a while coming but it's great to get things sorted and I can't wait to get going now," said Wright to the club website after his move had gone through.
"I've really enjoyed my time with the club so far. There's a great bunch of lads here and we've got a top manager as well. "Training has been really good, we're looking sharp and we can't wait to kick the season off against Norwich on Saturday."
Chris Coleman also commented saying: "Stephen is a quality full-back and plays in a position that we needed to fill. He has played at the highest level and has looked very good for us during pre-season. "His experience will help some of our younger players and he is a great lad to have around the place as well."