The German midfielder has spoken for the first time since Juve announced on Tuesday that the player will join the Turin giants on a free transfer from July on a four-year deal.
Khedira’s contract with Real Madrid expires at the end of this month.
“Yesterday was a great day,” Khedira wrote on his Facebook page. “I am happy and excited to say that I will be playing for Juventus for the next four years.
“Juventus is a wonderful club with a great history. With Juve everything seemed to fall in place.
“My discussions with the coach (Massimiliano Allegri) and the club were great.
“I’m very happy to play in a team full of champions and with unbelievable fans. It’s a great club with a one of a kind tradition in a very special city!
“I can’t wait to begin this splendid adventure as a Bianconero! Forza Juve!”
Khedira turned down a contract extension with Real last year and made just 11 Primera Division appearances for the Spanish giants this season.
A World Cup winner with Germany in 2014, Khedira joined the Madrid outfit five years ago from Stuttgart and won La Liga, the Copa del Rey and Champions League titles during his first three seasons at the Bernabeu.
The 28-year-old becomes Juve’s second summer signing following the arrival of Argentinian forward Paulo Dybala from Palermo last week.
Juve are hoping to strengthen their squad as they look to repeat what has been a stunning campaign next season.
Under first-year coach Allegri, Juve won a fourth straight Scudetto and lifted the Coppa Italia this season – clinching the domestic double for the first time since 1995.
The Turin giants also reached the Champions League final for the first time since 2003 before bowing out in a 3-1 defeat to Barcelona on Saturday.