As reported by Goal in early May, the striker's move to Stamford Bridge was tied up following Chelsea's Champions League semi-final exit to Atleti - with the Blues paying around £35 million including agent's fees.
|15/8||Chelsea are 15/8 with bet365 to win the title this season|
The move has long been mooted, with Costa himself confirming the agreement exclusively to Goal in June: "Why would I have chosen to play for Chelsea? It is a thing that is about to happen.
"Things are going in a direction and, if they keep going as they are going, it is the team I will play for in the next season.
"I've wanted to play in the Premier League for a while. Chelsea are one of the greatest clubs of the world so there are many factors that make you take a decision like this."
Costa will become Chelsea's second signing of the summer following the capture of Cesc Fabregas from Arsenal, with Jose Mourinho also pursuing Juventus and France star Paul Pogba in a potential deal worth £60m.