The 33-year-old leaves Chinese outfit Shanghai Shenhua to sign a six-month contract, with Juve including the option of a further year.
A statement on juventus.com read: "Anelka is a Juventus player. His contract, which runs until June 30, has been submitted to the league.
"The agreement includes the option to renew the deal until June 30, 2014."
Anelka underwent a series of medicals in Turin last week but the deal was not ratified until this morning.
The Frenchman issued a brief statement on Juve's website, which read: "Juve are bigger than everybody else."
Juve becomes the 10th club of a career which has seen Anelka rack up estimated transfer fees of almost £85million, while also scoring 14 goals in 69 caps for France.
He was part of their victorious Euro 2000 squad and has won the Champions League with Real Madrid, league titles in England with Arsenal and Chelsea and in Turkey with Fenerbahce, and three FA Cups, two with the Blues and one with Arsenal.