The Sporting Kansas City forward will be with the Canaries until May 6 after getting his international clearance to join the Premier League side.
Kamara will be available for selection for Norwich City's clash with Fulham at Carrow Road on Saturday. He will remain on loan until May 6, at which point Norwich can either opt to purchase his contract outright from Sporting KC and MLS or have him return to the club where he has found his footing and emerged as one of the league's top attacking talents.
Kamara scored 30 goals in the last three seasons in Kansas City, including a career-high 11 last season.
The 28-year-old Sierra Leone international joins a Norwich side that has managed just 25 goals in 25 games, a scoring rate that is fourth-worst in the Premier League. Only Stoke City (24 goals), Aston Villa (23) and Queens Park Rangers (18) have found the back of the net with less frequency.