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.
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."
Kamara could make his debut in Saturday's Premier League clash with Fulham.
"Finally the time is here. I'm so excited," the Sierra Leone forward told Canaries Player ahead of his flight to the UK. "I've just got to get there, try to impress in training and try to get myself in a position where I can be on the field.
"I'm going to make it difficult for the coach, to have options and to give me a chance when the time comes."
Kamara, who had a trial at Stoke before Norwich made their move, has been training on his own in recent weeks to prepare for the move, including going to the gym during last Sunday's Super Bowl.
"It's really not that hard to keep yourself motivated, saying 'hey, I'm going to be playing in the Premier League'," he said. "It's a good motivation when you're in the workout room."
Kamara thanked his MLS side for the opportunity to move to Carrow Road. "I loved my time at Kansas," he said. "It's the best place for me; the best three years. I've had so much fun.
"But when you have a chance like this, to play in the best league in the world, there's no way they were not going to let me live my dream a little bit.
"Getting the chance to come over is surreal. I can't wait. It's time for me to test my skills with the top players. I'm a forward with a lot of energy, athleticism.
"I'm just really, really happy to get myself in front of goal. What I want to do is get chances to put the ball in the back of the net."
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.
Norwich boss Chris Hughton was enthusiastic about Kamara and speaking after the Spurs draw, Hughton said: "I think he'll give us another dimension in the forward area.
"He's a player that's done very, very well in the MLS over the last few seasons, scored a lot of goals, a lot of assists.
"From what I've seen of him, we're not just taking an average player from that division. We're taking a player from that division that has excelled in recent seasons.
"How quickly he can adapt, how much he can give us. We're quite looking forward to the prospect of seeing that."
Norwich are 14th in the Premier League, seven points clear of the relegation zone, but have just two wins from 12 in all competitions.