The Foxes had a reported ?£1.5million offer for Schmeichel accepted last week and the 24-year-old has signed a three-year contract to team back up with Foxes manager Sven Goran Eriksson, who he worked with at Notts County and Manchester City.
Leicester's football director Andrew Neville said: "Sven knows Kasper extremely well and regards him very highly, so we're delighted to have brought him to the club."
He added: "He's already made a big impression both domestically and internationally and is another player at a good age for our long-term objectives.
Schmeichel, who had a season left on his Leeds contract, had expressed his surprise that Leicester's offer had been accepted and initially said he had not sought to leave Elland Road, where he made 40 appearances after signing from Notts County last summer.
He is Eriksson's third summer signing following the arrivals of midfielder Neil Danns and defender Lee Peltier.
Source: PA
Source: PA