The Ghana international completed his medical on Wednesday and becomes Roberto Martinez's fourth signing this summer
The 22-year-old joined Chelsea from Porto last September but spent last season on loan Vitesse, where he was named the Dutch club's player of the year.
Everton had already signed Romelu Lukaku from Chelsea in a 35 million euro deal this summer, and has now completed a deal for Atsu, who passed a medical on Wednesday.
It was Great meeting the manager after a successful medical test at Everton. pic.twitter.com/FMser7Il6c— Christian Atsu (@ChristianAtsu20) August 13, 2014
"I'm very happy to be joining Everton because it's a great club, which likes to play football, and it's a great pleasure to be here," Atsu told the club’s official website.
"Playing in the Premier League has always been a dream for me and I have achieved that dream.
"This is the biggest level for me to play at. I know that it's a very competitive league and I believe with hard work we're going to be successful this season."
The Ghana international becomes Everton's fourth signing this summer following the arrivals of Lukaku, Muhamed Besic, and Gareth Barry, who has joined on a permanent deal from Manchester City after spending last season on loan at Goodison Park.
"He's a player who fits in with the culture and the way we want to play. He's a very gifted technical footballer and he's got the right personality and character to fit in with the group, which is vital," said Everton boss Roberto Martinez.
"He will excite fans because he brings something completely different and a different way of playing to what we've got in the squad.
"He's a left-footed player who loves taking people on and he's got a really good understanding of the game for such a young man.
"He also brings extra competition in a position in which we felt we needed a player full of desire and hunger, who really wants to make things happen in the final third of the pitch.
"For Christian, at 22, to already have played in a World Cup, to have been able to adapt into Portuguese football and into the league in Holland is a really good accumulation of experiences that will be very beneficial, especially with us playing in the Europa League this season."