Can, who joined Liverpool in 2014, made his 167th and final appearance for the Merseyside outfit when he came on as a substitute in their Champions League final defeat by Real Madrid last month.
He has been capped 20 times by Germany but missed out on Joachim Loew's World Cup squad.
Can becomes Juve's second signing of the close season following the arrival of goalkeeper Mattia Perin from Genoa.
(Reporting by Hardik Vyas and Aditi Prakash in Bengaluru; Editing by John O'Brien and Ian Chadband)
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