The 20-year-old was at Goodison Park on Saturday to watch Everton‘s 1-0 defeat by Chelsea in their opening Premier League game of the season.
West Ham was also attracted to Onana and had agreed on a fee for the player.
“It feels great to join Everton,” he told Everton TV. “I know it’s a big, big club, one of the biggest in England. It’s something I want to be part of for many years.”
Onana becomes Everton’s fifth signing of the summer after James Tarkowski, Dwight McNeil, and loan pair Ruben Vinagre and Conor Coady.
Onana, who made his Belgium debut against the Netherlands in June, said Everton manager Frank Lampard was a key figure in his decision to move.
“Everyone here showed they wanted me and they have a plan for me,” he explained.
“I appreciated the talks I had with the manager and director of football (Kevin Thelwell). They told me how they wanted me to play and I enjoyed it.
“The manager played at the highest level, won many things, and was a midfielder too. It means a lot to have an interest in him and I think he can teach me many things.
“They both have a lot of ambition and that’s the type of guy I am, so it matches.”
Lampard said: “Amadou is a player we were keen to bring to Everton.
“He has many great qualities to help bolster our midfield and, at just 20 years old, has huge potential to get even better.
“I spoke to him about why Everton was the right club for him and we’re all looking forward to him showing what he can bring to the team.”