Costa, a key figure in Chelsea's two titles in the last three seasons, has not featured for the club since the FA Cup final defeat against Arsenal in May.
"Chelsea Football Club has today agreed terms with Atletico Madrid for the transfer of Diego Costa," a statement said.
"The transfer will be subject to the agreement of personal terms and a medical."
According to Spanish paper El Mundo, Atletico will pay €55 million ($NZ89 million) for Costa, making him their record signing, surpassing the €40 million they paid Porto for Radamel Falcao in 2011.
The 28-year-old Brazil-born forward joined Chelsea in 2014 and scored 52 goals in 89 league appearances.
Costa finished as Chelsea's top scorer for each of his three seasons in London, but while his contribution on the field was huge his time at Stamford Bridge has not always been harmonious.
In his second season his sudden loss of form was a contributory factor in the poor start to the campaign which ended in the sacking of coach Jose Mourinho.
After winning a second Premier League winners' medal last season he made clear his wish to rejoin Atletico during the summer after claiming Chelsea manager Antonio Conte had told him via text message that he was no longer required at the club.
Rather than returning to London for pre-season training he opted to remain in Brazil, accusing Chelsea of treating him "like a criminal" and asking for an unrealistic transfer fee.
Problems arose at the start of the year when Costa was left out of the Chelsea side for an away match at Leicester City after reports of a training ground dispute with a fitness coach.
At the time Costa seemed on the verge of signing a lucrative deal with Chinese Super League club Tianjin Quanjian. He returned to the first team, however, and ended the season with 20 Premier League goals as Chelsea lifted the title.
During the summer transfer window Chelsea signed a natural replacement in Alvaro Morata from Real Madrid.
Costa will have to wait before pulling on the red and white striped shirt of Atletico as the European transfer window is closed and Atletico are banned from registering new players until 2018 after breaching FIFA rules.
He will be eligible for selection from January 2 when the Spanish transfer window opens and Atletico's ban ends.
Costa first joined Atletico in 2006 and following a string of loan spells established himself as a key part of Diego Simeone's title winning side in 2013-14 before joining Chelsea in a deal worth £32 million pounds ($NZ52 million).
Atletico are in the same Champions League group as Chelsea but their two clashes will both be before Costa is eligible to continue his career with the Spanish club.
