The 24-year-old joins the Turin giants for a fee of €9million and has signed a four-year contract.
Elia becomes the third Dutchman to play for Juve. "I hope I can do as well as them," said Elia, who follows in the footsteps of Edgar Davids and Edwin van der Sar.
"I want to show what I can do. I know I can bring speed and skill to Juventus, and I hope to score a lot of goals."