The Blancos confirmed the signing of the left-back for a fee of £47 million ($59m) on Wednesday, taking their summer spending to almost £300m ($378m) after completing deals for Eder Militao, Rodrygo, Luka Jovic and Eden Hazard.
The 24-year-old joined Les Gones from Ligue 2 outfit Le Havre and became one of their key players as they finished third in Ligue 1, with Aulas telling Radio MARCA: "He arrived at Lyon two years ago from Le Havre.
"He started to play for France when he was just 22; his rise has been very quick.”
The Lyon president also revealed that he shares a healthy relationship with his opposite number at Real Madrid, which only helped facilitate a smooth transfer.
"Florentino Perez and I are very good friends, and this always influences negotiations," he added.
Zinedine Zidane is wasting no time in attempting to re-assert his side as a dominant force in Spain after they failed to mount a title challenge against Barcelona in La Liga, as well as exiting the Champions League in the round of 16 against surprise package Ajax.
It was the France legend’s call that convinced Mendy to make the switch, Aulas confirmed, adding: “It was Zidane's request, yes.
"When he called [Mendy], he couldn't resist."
"It's up to Zidane to decide! [whether Mendy starts over Marcelo]"
Mendy made 79 appearances for Lyon across two seasons, scoring three goals as the club made their Champions League return ahead of the 2018-19 season.
The Frenchman also made his international debut last season, starting in a 1-0 friendly win over Uruguay before going on to make his competitive debut in Les Bleus’ 2-0 defeat to Turkey in Euro 2020 qualifying.
Aulas has chosen not to dwell on losing the 24-year-old, and has already signed his replacement ahead of the 2019-20 season.
"We've signed another player, Heritier Deyonge [from PSV Eindhoven], who has the same characteristics and is a prospect for the future," he continued.
"He's Belgian and is 17 years old."