The 27-year-old called time on an 11-year stint with the Gunners in July, having found opportunities limited for the previous two seasons following Petr Cech's arrival.
During his time with Arsenal, Szczesny won two FA Cup trophies, whereas in the equivalent period, Juve claimed six consecutive Serie A titles and three back-to-back Coppas Italia.
"I came here because I need to win everything," he is quoted as saying by Mediaset. "I chose Juventus for their winning mindset. Every day in training I feel stronger and more ready to play for this club.
"It seemed a normal choice to me, when Juve call you, you have to go. When you play for Juventus the goal is always to win everything, and it's no different this year."
Szczesny has made just two Serie A appearances for his new side so far this term.