They accidentally met at a Milan hotel when Inter Milan defender Materazzi was going to meet former boss Jose Mourinho, who was in the city for Real Madrid's Champions League game with AC Milan.
Rumours have since persisted that Zidane, a Real adviser, bumped into Materazzi and the former Italy international has now confirmed the speculation.
"What was said stays between us. Let's say I did most of the talking and when at the end he held out his hand, I shook it firmly until he looked me properly in the eye," Materazzi told Mediaset television.
"It's what I wanted. For me it was great, I don't know about him."
Zidane was sent-off for butting Materazzi in the chest in the 2006 final, the last match of his career. Italy won 5-3 on penalties after a 1-1 draw.
Materazzi also revealed a number of run-ins with former Inter striker Mario Balotelli, who infuriated his team mates last term with his attitude and by being pictured wearing an AC Milan shirt.
"He received a slap and a boot in the face," Materazzi said of the Manchester City striker.
"But when he had an operation and he was in hospital, I was there at midnight keeping him company and getting him snacks from the machine."
