The 29-year-old, who is his national team's Player of the Year, has spent most of his career playing US Major League Soccer but enjoyed a spell on loan in the Premier League at Norwich City last season.
The fee is undisclosed.
Tony Mowbray said: "We are delighted that Kei's s here. He will add to our attacking options all across the front line.
"He'll bring some added power, pace and an aerial threat to our squad."
Describing a whirlwind weekend leading up to the transfer, Kamara told mfc.co.uk: "I played a game on Saturday, got on a plane on Sunday and now I'm here on Monday so it's been a long couple of days but now I'm delighted to be here.
"I've heard playing in the Championship is a lot harder than the Premier league but I'm always ready for a challenge so I'm looking forward to it. Hopefully my own style and way of playing will help the team out."
Kamara moved to the United States from his war-torn homeland as a teenager and as well as Kansas he has played for Columbus Crew, San Jose Earthquakes and Houston Dynamo.
Although he stands at an imposing 6ft 3ins tall, Kamara has played most of his football as a winger but he is also comfortable as a central striker.
Despite usually being deployed in a wide position he has been Sporting Kansas City's leading scorer for three consecutive seasons and has won a host of awards.
Known for his pace and power, he is also a menacing presence in the air and scored a stunning header for the Canaries against Everton.