Madrid paid €50 million to sign the French defender from Lyon as Zidane continues to revamp his squad after the disappointments of last season.
Mendy joins Eden Hazard, Luka Jovic, Eder Militao and Rodrygo in moving to Madrid as part of a €300-million summer spending spree ahead of the new season.
"It's an honour to be around a football legend like Zidane," Mendy said at a press conference.
"I followed him when I was little, I know very well what he did during his career and it is a great pleasure to be able to work with him."
Mendy had earlier signed his contract in the club's boardroom and posed for photographs in front of Madrid's 13 European Cups.
The 24-year-old came through the youth system at Paris Saint-Germain but an arthritic hip threatened to cut short his career. Instead, he moved to Le Havre before joining Lyon for just 5 million euros in 2017.
"When I was 15 years old, I had an operation on my hip," Mendy said. "They told me I was not going to play football again.
"I spent some time in a wheelchair, and six or seven months in the hospital to be able to walk again and now I am at Real Madrid. It's really incredible."
Club president Florentino Perez said: "We have brought you here because of the quality, talent, work and fight that have all characterised your life."
Despite his hefty price tag, Mendy is not guaranteed a starting spot under Zidane, with fellow left backs Marcelo and SerRead More
