Stewart, who played a key part in the Black Cats' Championship-winning side last season, was unveiled at an Ashton Gate press conference.
The 32-year-old is the latest capture for the League One promotion-chasers, and he will partner 29-goal Leroy Lita in the Robins' attack next season.
"I will now be playing for the team I loved as a kid. I didn't speak to anybody else because I made my mind up halfway through last season that I wanted to come to Bristol City," said the ex-Huddersfield and Ipswich forward.
"I didn't speak to any other club because I would have been wasting their time. The manager and the chairman wanted me and I'm delighted to be here."
He joins Torquay's Alex Russell, and Swindon duo Grant Smith and Matt Heywood in signing for the club.