Chelsea officially announce the signing of Diego Costa finally
The fee is undisclosed but in the region of £32m.
His goals helped Atletico claim a first Spanish league title in 18 years last season and he helped the Madrid side to the Champions League final, beating Chelsea in the semi-final en route to Lisbon, where Real Madrid won the European Cup.
Costa said on chelseafc.com: "I am very happy to sign for Chelsea.
"Everybody knows it is a big club in a very competitive league, and I am very excited to get started in England with a fantastic coach and team-mates.
"Having played against Chelsea last season I know the high quality of the squad I am joining.
"I would like to thank everybody at Atletico who made me into the player I am, it was an incredible time for me, but now I am starting a new adventure and I hope to win many trophies with Chelsea."
Costa is one of a number of players who featured for Atletico last season who could be plying their trade for the Blues next term.
Belgium goalkeeper Thibaut Courtois spent three years on loan with Los Rojiblancos and is expected to compete with Petr Cech for Chelsea's number one jersey.
Brazil left-back Felipe Luis is the subject of interest from the Blues, who are seeking a replacement for Ashley Cole after the former England defender's move to Roma.
Portuguese midfielder Thiago has also been linked with a Stamford Bridge return from Atletico.
Departures are likely, too. Demba Ba's future at Chelsea is in doubt, with the striker linked with Turkish side Besiktas.
Ba could feature for Chelsea in Wednesday night's friendly with Wycombe when Jose Mourinho will assess his fringe players, including many of those who spent last season on loan.
The first group of players involved in the World Cup will join up with Chelsea for the pre-season tour.
The Blues play RZ Pellets on July 23 before matches in Slovenia, Holland, Germany and Hungary.