The 24-year-old striker scored eight goals in 29 appearances for Sunderland last season after moving to the Stadium of Light on a temporary deal.
Juventus, who went the entire 2011-12 league campaign without suffering a defeat, have been looking to add a striker to their ranks, with the Turin outfit previously showing interest in Robin van Persie and Luis Suárez.
“I can now finally say I am a Juventus player. Very proud and can’t wait to wear the stripes! I hope we will have great times together,” Bendtner posted on Twitter.
“I want to fulfil my potential here and show the fans my absolute best as that is yet to come. I am sure I will.
“Thanks for all the support from the Arsenal fans and the Sunderland fans, means the world. We always believe and that gets us far!”
Bendtner has scored 43 goals for the Gunners in seven years at The Emirates, with the Dane spending successful loan spells at Birmingham City and Sunderland.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news