The 22-year-old, who made his debut for the Toffees in May 2016, played second fiddle to Seamus Coleman last season and was restricted to just 13 appearances across all competitions.
The Bundesliga side announced the arrival of the right-back via a humorous social media post that riffed on the "oh my god, they killed Kenny" catchphrase from TV show South Park.
Kenny, who is on duty with England ahead of the European Under-21 Championships, told the club's official website: "It is a big chance for me, to come to a new country and show off my abilities, especially at a big club like Schalke.
"Schalke is a club with a long history and fantastic fans. I am happy to be here and can't wait to get up and running with the team."