Manager Roberto Martinez revealed earlier in the week the contract had been concluded "in principle" but the news was made official on the club's website on Wednesday night.
The 22-year-old Ghana international passed a medical on Wednesday and having secured a work permit will be available immediately for duty, with his new team travelling to newly-promoted Leicester on Saturday for their Premier League opener.
Atsu told evertontv: "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.
"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 move means a second successive year on loan for Atsu, who moved to Stamford Bridge from Porto for £3.5million last summer, but then headed out to Vitesse Arnhem.
Martinez has insisted during the summer that one of his transfer priorities was for a wide man in the squad.
On his latest acquisition, the Spanish boss said: "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.
"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."
Martinez added: "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."