The pair have had a long-running feud since the 2006 World Cup final when Zidane was sent-off for headbutting Materazzi in the chest.
That was the then France captain's last ever professional match as a player and he later claimed he had reacted to slurs the Italian directed against his sister.
Last month, ahead of Milan's Champions League clash against Real Madrid at the San Siro, a Spanish journalist claimed to have seen the pair shake hands and make up at a Milan hotel, although Zidane later denied this.
But now Materazzi claims that such an exchange did indeed take place.
"I was leaving the hotel when someone came and stopped me and said there was a problem," he told Mediaset on Thursday.
"They said that Zidane was parking right next to my car. I replied that I didn't see a problem.
"I went out and found myself in front of Zidane so I took the opportunity to say some things to him, things that he and I know and that will stay between us.
"Let's say that it was I who spoke most and at the end when he extended his hand to me I clasped it and didn't let go until he looked me properly in the eye.
"That's what I wanted and that's how it went."
Materazzi, who plays for Inter Milan, had gone to Real's hotel to greet his former boss Jose Mourinho while Zidane now has a coaching and consultation role at Real.