The 21-year-old has penned a five-year deal after impressing for Porto as they won the Portuguese league last term and will now join the Eredivisie side on a season-long deal
The 21-year-old midfielder will move to Eredivisie side Vitesse Arnhem on loan for the rest of the season.
Liverpool were in pole position to sign the Ghana international before displaying a reluctance to meet the Portuguese club’s €4 million asking price for a player who has just a year left to run on his current contract.
Atsu becomes Jose Mourinho's seventh summer signing since rejoining the club for a second spell following the arrivals of Cristian Cuevas, Samuel Eto'o, Andre Schurrle, Mark Schwarzer, Marco van Ginkel and Willian.
The attacker made his first-team breakthrough at Porto last term, clocking up 17 appearances as the club won the Portuguese league, and will now look to continue his development at Vitesse due to the fierce competition for places at Stamford Bridge.
Question marks continue to be raised over Juan Mata's future at Chelsea after limited playing time so far this season, but Mourinho has insisted the two-time Player of the Year is not for sale.
Elsewhere, Victor Moses has been linked with a move to Liverpool ahead of Monday's transfer window deadline.