The offer had been in the pipeline for a quantity of months, and the clubs agreed a fee before in July, with the go now verified by the Premier League club.
The fee for the Brazil-born participant, who represented Spain in the Globe Cup, has not been uncovered but it is considered to be in the location of 32million.
"Chelsea Football Club is delighted to announce Diego Costa has these days done his transfer from Atletico Madrid by signing a five - calendar year agreement," study a statement on the clubs official web site.
"He will be part of up with the initially workforce for our pre- season European education camp subsequent 7 days."
Costa was delighted to see the shift eventually finished and is keen to test himself with a club he confronted as an Atletico participant previous period.
Costa scored the 2nd target in the Spanish sides 3 - one get at Stamford Bridge in their UEFA Champions League semi- ultimate 2nd leg match past year to support safe their closing place in the ultimate versus rivals Authentic Madrid.
The twenty five - calendar year - previous also scored 35 objectives previous period to aid Atletico win their very first Spanish league title in 18 several years and he is now prepared to start off his clean problem in the Premier League.
"I am really happy to sign for Chelsea, stated Costa.
" Everyone is aware of it is a big club in a extremely competitive league, and I am really enthusiastic to get started off in England with a wonderful coach and crew -mates.
" Having performed towards Chelsea previous time I know the significant top quality of the squad I am joining.
"I would like to thank everyone at Atletico who designed me into the player I am, it was an unbelievable time for me, but now I am starting a new adventure and I hope to earn many trophies with Chelsea."
Watch Chelsea's opening video game of the new time away to Burnley on Monday August eighteen on Sky Sports one.