The France left back, 24, joined Real last week from Olympique de Lyonnais for a reported 48 million euros, part of a huge squad rebuild by the 13-times European Champions which has already surpassed 300 million euros.
"When I was 15 years old I had a hip operation and they told me I wasn't going to play football again," Mendy said.
"I was in a wheelchair for a while and I spent between six and seven months in hospital doing rehabilitation so I could walk again. Now I'm at Real Madrid and it's really incredible."
Mendy has experienced a dramatic change of fortunes in the last two years, after beginning his career in the second tier of French football with Le Havre until joining Lyon in 2017.
He made his debut for France last November and has made four appearances for the 2018 World Cup winners, but he said he still had to pinch himself.
"At the beginning I just couldn't believe it," he added.
"This is a great club and being able to sign a contract with them to me is something absolutely incredible, fantastic. I'm absolutely overjoyed and hopefully everything will go well here."
(Reporting by Richard Martin, editing by Ed Osmond)
