The 27-year-old winger joins on a two-and-a-half-year deal, through to June 2018, for an undisclosed fee.
The move to Ewood Park sees Bennett reunited with Rovers boss Paul Lambert, who signed him from Brighton whilst in charge of the Canaries in June 2011.
Bennett began his career with Wolves, but was restricted to just a couple of League Cup appearances, plus loan spells away from Molineux with Crewe and Bury.
He joined Brighton in August 2009, scoring eight goals in his first season and then nine in his second, as the Seagulls secured the League One title.
Having made exactly 100 appearances for the south-coast club, Premier League new boys Norwich came calling in the summer of 2011.
Bennett featured regularly under Lambert in his maiden season at Carrow Road, making 22 starts and 10 substitute appearances as Norwich secured a 12th-place Premier League finish. He also netted a spectacular strike in a 2-1 win over Spurs.
The midfielder made 24 Premier League appearances the following campaign, as the Canaries finished 11th, however a cruciate knee ligament injury sustained on the opening day of the 2013-14 season halted his progress in a Norwich shirt.
Following their relegation to the Championship, he rejoined Brighton on a short-term loan in November 2014, before returning to Norwich in the New Year and playing his part in their promotion to the Premier League via the play-offs.
Earlier this season, Bennett linked up on loan with Bristol City, where he has started 15 Championship games and played against Rovers in the game at Ashton Gate last month.
The new signing is expected to go straight into the squad for Saturday’s FA Cup third round tie away to Newport County.
Earlier today, Rovers secured the services of Welsh international Tom Lawrence from Leicester City for a further month.