The 22-year-old winger played against City twice last year and says that those two games left him desperate for a move to Steve Cotterill's side.
Speaking to the club's official YouTube channel, Freeman said: "It's a massive club, it's a great city and from playing against Bristol City last season, the two games against them made a real impression on me. That's why I've chosen to come here.
"I was impressed by the team and the ability of the players and I definitely didn't think twice about coming here.
"I knew there was interest in January and I'm not sure quite what happened with that, but I'm just happy to have it completed today.
"I believe there were a few setbacks and hurdles that needed to be jumped, but I was always confident it could be done - it was more a case of agreeing terms between the clubs."
The former Arsenal man, who joins from relegated Stevenage, is the third signing at Ashton Gate this summer