The Poland international was formally presented as a Juve player at a press conference in Turin on Wednesday after passing a medical at the Serie A club.
Szczesny impressed while on loan in Italy with Roma over the last two seasons, and has opted to remain on the peninsula with the Bianconeri after reportedly signing for £14m.
"I'm delighted to be at Juventus. I've spoken to Gianluigi Buffon, a true legend of the game," Szczesny told a news conference. "When you join Juve, it's because you've been chosen. I didn't hesitate one moment before coming here.
"I'm ready to take on this challenge, Juventus is the best possible choice for my career. I'm 27 years old and I want to win. At this club there's the right mentality to do so. I hope that we'll succeed in winning the Champions League."
Szczesny joined Arsenal's academy from Legia Warsaw in 2006 and has made a total of 181 appearances for the Gunners.