The value of Szczesny's transfer could eventually rise to €15.3m depending on certain conditions being met over the course of his contract.
Szczesny has spent the past two seasons in Serie A on loan at Roma.
He joined Arsenal from Legia Warsaw as a youngster and went on to make 181 appearances in all competitions before the arrivals of David Ospina and Petr Cech left him looking elsewhere for first-team opportunities.
Szczesny's path to the starting XI at Juve is likely to be blocked by an all-time great, with Gianluigi Buffon preparing for a career swansong in 2017-18.
"I'm delighted to be at Juventus," he told a news conference. "I've spoken to Gigi Buffon – a true legend of the game.
"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."
Juventus lost a second Champions League final in three seasons against Real Madrid in Cardiff last month and Szczesny wants to help get a side so dominant at home during the present era over that hurdle.
"I hope that we'll succeed in winning the Champions League," he added.