King joined Wolves from Northampton Town in July 2023, spending two years at Molineaux before his departure on Saturday.
The 30 year-old made his Wolves debut in the final Premier League game of last season against Brentford. He also earned a first Wales cap last term.
King has signed a two-year deal with the Toffees and said: “I’m absolutely delighted to join Everton. From the moment I heard of the interest, it’s all I have thought about.
“We have two extremely good goalkeepers here in Jordan (Pickford) and Travs (Mark Travers) and a young keeper in Harry (Tyrer). My job is to push them as far as possible.
“The chance to learn off someone like Jordan, who has been England’s number one for so many years, is a really big thing for me. I’ve come from a great goalkeeping unit already and I’m walking straight into another one at Everton.
“It’s a chance to learn off Jordan and Travs, support Harry as much as I can, and, with my experience of playing through all the leagues and experiencing international football, help keep levels high every single day.
“It’s such an exciting time for Everton, with the world-class stadium, too, and I can’t wait to get going and be a part of it.”