The 26-year-old becomes Norwich's first signing of the transfer window, as manager Neil Adams looks to build a squad capable of achieving an immediate return to the Premier League following their relegation last season.
Grabban will remain at Carrow Road until at least 2017, with the option of an extra year, and joins for an undisclosed fee pending the completion of paperwork.
Speaking to the club's official website, Grabban said: "It's good to start a new chapter, get going again with Norwich and hopefully get promotion.
"I've played here before and the atmosphere's been great, the fans are great. It's exciting to be a part of the club now and hopefully do well for them."
Adams added: "Lewis possesses precisely the type of attitude, application and quality that I expect from my players. I am really looking forward to integrating him into the squad."
Grabban made 93 appearances for Bournemouth, scoring 35 goals.
He was among the leading scorers in the Championship last season, finding the net on 22 occasions.
