The 27-year-old forward has signed a three-and-a-half-year deal with the Cherries for a reported fee of around £7million.
Grabban returns to Vitality Stadium having spent two years in Dorset between 2012 and 2014, following Benik Afobe to the south coast club after his transfer was confirmed on Sunday.
A statement from Bournemouth read: "AFC Bournemouth have completed a deal to bring striker Lewis Grabban back to the club from Norwich City for an undisclosed fee, subject to Premier League clearance.
"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."
BREAKING: #afcb have completed a deal to bring @grabbs22 back to the club from #ncfc: https://t.co/wfhDAKbJxZpic.twitter.com/yEuEiYlPq5
— AFC Bournemouth (@afcbournemouth) January 11, 2016