The 22-year-old Ghana international could make his debut in the opening league game of the season against Leicester City on Saturday.
"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 Evertontv. "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."
Atsu became Everton's fourth recruit of the close season following striker Romelu Lukaku, also from Chelsea, former England midfielder Gareth Barry and Bosnian midfielder Muhamed Besic.
"He's a player who fits in with the culture and the way we want to play," Everton manager Roberto Martinez told the club's website. "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.
"He will excite fans because he brings something completely different and a different way of playing to what we've got in the squad."
Atsu started his career in Portugal with Porto before joining Chelsea in 2013.
He spent last season on loan at Dutch club Vitesee Arnhem and started all three of Ghana's matches at this year's World Cup in Brazil.
(Reporting by Ed Osmond; Editing by Frank Pingue)
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