Juve and Real will meet in the Champions League final on Saturday in Cardiff.
Del Piero recalled: "How was Zidane as a teammate? He was a special person. There was a harmony, a different understanding between us on the human aspect.
"Zidane had an extraordinary talent, which contributed to his sole interest in helping the team. He was not a selfish player. He had a unique ability to be a great and to be a team player. I was lucky to play with him.
"When we shared the same locker room, I could not imagine that he would take this path (become a coach). But when I saw him on the bench, I honestly thought he could do well. He is intelligent, ambitious and sees football with great lucidity, so he has the ability to make the right decisions both on and off the field.
"The results speak for him. He has won everything so far."