In a deal reportedly worth around £1.7million, the Premier League winner has signed a three-year deal at Goodison Park.
Gray will therefore be contracted to the club until the end of the 2023-2024 season, with Everton having an option to extend that by a further year.
The 25 year-old joins Andros Townsend and goalkeeper Asmir Begovic as the first arrivals ahead of the 2021-2022 season under new manager Rafael Benitez.
"I'm delighted to be back in the Premier League at such a big club and I'm excited to play with the team and get to work," Gray said. "Speaking to the manager and [Director of Football] Marcel Brands, I had a really good feel for the Club and I feel this is a place where I can continue to develop.
"The manager, with his ambition and what he has won in the past, is important and we’ll look to push forward and compete with the top clubs. I think a club of this magnitude has all the potential to be right up there.
"Everton are a very big club and the main objective is to be pushing and competing back up there in the table.
"I want to work hard on the training pitch and work my hardest for the club on the pitch."
Gray, who will wear the number 11 shirt for Everton, only spent six months in Germany and made 12 appearances for Leverkusen, scoring once.
He has linked up with Benitez's squad in Florida ahead of Everton’s participation in the Florida Cup.
Everton was due to face either Arsenal or Inter after playing against Colombian side Millonarios, but the Gunners and the Serie A champion pulled out of the competition due to coronavirus concerns.