The defender has arrived from Hellas Verona in a deal rising to €15m.
The Colombia international told Juve's website: “I am very happy, as this is one of the biggest clubs in the world and I am so overjoyed to wear this jersey.
“As a kid, I wore this jersey that was not an original one, and now I get to wear the legendary Juventus shirt and I am so happy. I was always a Juve fan.”
He added, "My objective at Juve is first of all to get enough space to play and then win everything with this club. I talked to the coach this morning, he is very nice. He was a player not too long ago and a wonderful one, so I told him that he’s great for the way he works and I want to be a great player here at Juve.
“Everyone in Colombia is celebrating, because this is an important step for me, my family and all the kids who also have a dream and can see me making it happen.”