The 28-year old's move from Major League Soccer to Carrow Road until May 6 was announced last week, subject to receiving immigration clearance, which has now been granted, the Canaries have announced.
The club wrote on Twitter: "@norwichcityfc are pleased to confirm forward @keikamara has been granted a visa to join us on loan from Sporting Kansas City."
A statement on the club's official website added: "City are pleased to confirm forward Kei Kamara has been granted a visa to come and play for Norwich City on loan from Sporting Kansas City until May 6.
"The 28-year-old Sierra Leone international will fly into the UK to join his new Canary team-mates over the next 24 hours and will be available for selection for Saturday's Barclays Premier League clash against Fulham at Carrow Road."
The deal for Kamara was agreed last Wednesday, ahead of the 1-1 draw with Tottenham, and Luciano Becchio followed from Leeds 24 hours later on transfer deadline day.
Kamara wrote on Twitter: "Happy to say I have picked up my passport/visa & getting on a flight tonite to England."