The 28-year-old is one of the most highly rated defenders in the second tier and he becomes the club's second signing of the summer after former Manchester United midfielder Paddy McNair joined Tony Pulis' side for roughly £5m from relegated Sunderland.
Flint was in demand this summer and Middlesbrough have confirmed that they had to fight off a number of other sides to land the defender on a four-year contract at the Riverside.
The defender made 46 appearances for Bristol City last season, scoring an impressive nine goals across all competitions as the Robins finished in mid-table.
Flint has lifted the Football League Trophy during his five-year spell at the club. The Englishman was voted into the League One Team of the Season as Bristol City were promoted to the Championship where he has since been crowned as the club's Player of the Year on two occasions.
The 28-year-old will now travel to Austria to link up with his new teammates at Middlesbrough's pre-season training camp, where they will take on domestic side SK Sturm Graz - who qualified for the second qualifying round of the Champions League last season.