The 30-year-old international from Senegal would be eligible to play for the Foxes in the Championship play-offs should Leicester reach them.
Sven-Goran Eriksson's side have moved into the top half of the table, and the Swede said that the addition of Kamara would give the team much-needed experience.
"Diomansy is a quality striker and will be a great addition to our team," Eriksson said.
"He brings with him pace, good technical ability and of course, Premier League quality.
"I am sure he will settle in well and will be an exciting player for the club."
Having struggled to break into the first team for the Cottagers in recent times, Kamara also had a loan spell last year with Celtic.