The Germany international failed to agree terms on a new deal with Los Blancos last summer and saw little game time under former coach Carlo Ancelotti during the 2014-15 campaign, much to the midfielder's frustration.
Khedira had been linked with a return to the Bundesliga, with Schalke, while Premier League sides Chelsea and Arsenal were also said to be interested, but the World Cup winner has now elected to move to Turin.
"Juventus Football Club has today completed the signing of Sami Khedira," read a statement released on the Bianconeri's official website on Tuesday.
"The 28-year-old, who will officially join from Real Madrid on a free transfer on 1 July 2015, has agreed terms on a four-year contract which expires on 30 June 2019.
"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.
"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."
Khedira will compete for a starting berth with Claudio Marchisio, Arturo Vidal, Andrea Pirlo and Paul Pogba.
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