Szczesny, who now formally ends his association with the Gunners after 11 years, was unveiled to the press in Turin on Wednesday afternoon after undergoing a medical earlier in the week.
He has signed a four-year contract to 2021 and is initially expected to fill the role of understudy to legendary veteran and current number one Gianluigi Buffon.
"I'm delighted to be at Juventus. I've spoken to Buffon - a true legend of the game," Szczesny said to the press upon his arrival.
"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," he added.
"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."
Former number two Neto joined Valencia in a €6m deal earlier this month.
Szczesny has been playing regularly in Serie A since 2015 after spending the last two seasons on loan with Roma and has established himself as one of the best goalkeepers in the division.
The 27-year-old is the third new face to join Juve so far this summer after Douglas Costa's loan from Bayern Munich and Rodrigo Bentancur's arrival from Boca Juniors. Juan Cuadrado and Medhi Benatia have also seen their loans made permanent since the end of last season.
Confirmation of Mattia De Sciglio's arrival from Milan is also imminent after the versatile full-back arrived in Turin for his medical on Wednesday morning.