Manager Roberto Martinez had made no secret of the fact that a deal was imminent for the 22-year-old and he has now got his man after the Ghana international passed a medical on Wednesday night.
Atsu has also been granted a work permit and will be available when the Toffees travel to Leicester for their Barclays Premier League opener on Saturday.
Both clubs confirmed the deal on their respective websites on Wednesday evening and Atsu admitted he cannot wait to get started at Goodison.
"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," he 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's arrival will supplement the resources Martinez already has at his disposal, led by marquee summer signing Romelu Lukaku - also from Chelsea.
Striker Arouna Kone is still at least a month away from fully recovering from a knee injury which kept him out for most of last season while Kevin Mirallas, like his Belgium team-mate Lukaku, is still getting up to speed having returned to training later than many of his team-mates due to his World Cup commitments.
Steven Naismith is another alternative up front or off the right but Atsu will give Everton something extra in the same way Barcelona forward Gerard Deulofeu did in his loan spell last season.
"He's a player who fits in with the culture and the way we want to play," said Martinez.
"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.
"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."
Atsu is the fourth new arrival for Everton this season, following Lukaku, Gareth Barry and Muhamed Besic into Goodison.
He joined Chelsea from Porto last summer and spent last season on loan at Vitesse Arnhem before starting all of Ghana's World Cup games in Brazil this summer.
Source : PA
Source: PA