"Khedira, who is normally deployed in front of the defence as a ball-winning midfielder, is able to cover a lot of ground while also possessing excellent passing and shooting ability and great vision of the game," Juve said.
"Bianconeri boss Massimiliano Allegri is set to add a player of class, quality and international experience to his ranks, ready to enrich one of the strongest midfields in world football."
After joining Real from VfB Stuttgart in 2010, Khedira had a reasonably successful five-year stint with the La Liga club but fell out of favour after talks on a contract extension failed.
Last month, he accused Real of freezing him out by dropping him from the team even though he was fit to play.
He barely featured since the turn of the year, with Real citing a series of minor injuries as the reason for his absence, but Khedira said the club had decided he was no longer wanted.
"I've always felt that I've had the coach's backing, but the message indirectly came through to me that I was no longer needed, I was frozen out and wouldn't have a chance to continue playing," he told Marca sports daily.
"It hurts that I'm accused of a lack of professionalism because I've always put the team ahead of myself," he added. "I've always gone with the truth."
Khedira's move to Juve could facilitate the exit of their France midfielder Paul Pogba, who is reportedly a target for clubs including Real, European champions Barcelona and several English teams as well as Paris St Germain.
(Reporting by Ed Osmond and Iain Rogers, editing by Justin Palmer)
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