Grabban, who previously played for the Cherries between 2012 and 2014, returns on a contract until June 2019 after a year-and-a-half at the Canaries.
The striker netted 35 goals during his two season stay at Vitality Stadium, averaging a goal every 2.3 games.
In his final season for the club, Grabban was the Cherries’ leading goal scorer with 22 strikes, helping Eddie Howe's side secure a 10th-place finish in the Sky Bet Championship a year after being promoted from League One.
He was also voted AFC Bournemouth’s Players’ and Supporters’ Player of the Year for 2013/14.
The 26-year old then went on to score 13 goals for the Canaries after leaving the Cherries, helping them to promotion last season and scoring a crucial equaliser against Arsenal this season.
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