Welsh had spent most of his career at Stockport were he made 81 appearances for the northern club before switching to Sunderland in 2004.
Speaking to the clubs official site City manager Rob Kelly said :-
"I first knew of Andy when he was at Stockport County. We had a look while I was at Blackburn, but we were unable to do anything at that time and I've followed his progress since. He's a quick, direct left-sided winger. He's got a good attitude and I am sure he will help us in our battle against relegation.
"As soon as we made our interest known he wanted to come here and that's always pleasing. He's keen and has an appetite to come and play for us."
The deal should be completed later today.