Following the signing of goalkeeper Joe Cracknell this week, Leigh, 20, completed his own move to the Coral Windows Stadium this Thursday.
Like Cracknell, Leigh will now come into contention for a place in Phil Parkinson's travelling party for the club's season opener at Swindon Town this weekend.
Leigh has featured in a number of City's pre-season friendlies this summer, scoring the opener in the 3-0 over Motherwell during the club's week-long tour of Scotland last month.
He spent last season on loan at fellow Sky Bet League 1 side Crewe Alexandra from Premiership giants Manchester City.
After leaving the Ethiad Stadium in the summer, Leigh now becomes City's ninth signing ahead of the new campaign.
Parkinson said: "Although we already have Alan Sheehan and James Meredith for that left back slot, we just feel Greg has the ability to become a asset to the squad going forward.
"He has real power and pace, and he played a large number of games in League 1 last season for Crewe still at a young age.
"He may have to go out on loan for a month or so if he doesn't force his way into our team but we are confident he is a player who will improve.
"Greg has a great hunger and desire to be as good as he can be, and he'll be determined to try and force his way into that first team reckoning."