The attacker was meant to be the next big thing at the Clarets, but he failed to get enough game time for Sean Dyche's men.
The Bermuda international hopes that he can get back in the Premier League with Bristol to put things right.
He played for Burnley for two and a half years, managing only nine appearances and zero Premier League starts in that time.
"I had a Premier League opportunity, I didn't really get to take it so that's something that burns me deep inside," said Wells, speaking to Bristol Live.
"This club (Bristol City) matched my ambition to continue to move forward, not settling with just being in the Championship.
"This club wants to get to the Premier League and my ambition is the same. I want to give it everything I've got and this club gives me a very good platform of doing that.
"To have that taste of the Premier League … I had always dreamt of being there.
"Most players will have that drive and, for me, it's something that doesn't sit too well for me; that I got a move to the Premier League and I wasn't really able to stamp my authority and show what I had.
"To not be able to score Premier League goals still sits in the back of my head, always.
"We all have personal attributes but I'm always hungry to score goals. I'm very easy to complement a lot of players, I'm different to what we have here.
"I tick that box in what the club needed. I'm not content with just settling and being a good Championship player, I want to keep striving to get back to the Premier League and the ambitions of the club are equally aligned with that."