After three productive years at Stamford Bridge, the Spain international has been cleared to return to the club that sold him to the Blues for £32 million in 2014.
Costa won two Premier League titles during his time at Chelsea, netting 20 times in each of those campaigns, but was deemed surplus to requirements by Antonio Conte at the end of 2016-17.
The 28-year-old has had to wait patiently for a sale to be sanctioned, with the issue forced as he remained AWOL in Brazil, but Terry has paid an emotional tribute to his former colleague.
He posted on Instagram: “Good luck Diego Costa in your next journey my friend.
“An unbelievable player and one of the nicest and funniest guys I have met in football, playing against him in training and games was an absolute nightmare, one of the best and underrated players I have played with and against.
“He gave everything for our club every time he wore a Chelsea shirt and was a born winner.
“Going to miss you mate. Good luck to you and your family.”
Good Luck @diego.costa in your next journey my friend An unbelievable player and one of the nicest and funniest guys I have met in football, playing against him in training and games was an absolute nightmare,one of the best and underrated players I have played with and against. He gave everything for our club every time he wore a Chelsea shirt and was a born winner. Going to miss you mate Good luck to you and your family JT @chelseafc
Goal revealed on Thursday that a deal to take Costa back to Atletico had been struck, with Chelsea later confirming the agreement.
A £57m fee will return him to the Spanish capital and offer him a clean slate at the end of a testing period in his career.
Costa admits that his exit from Stamford Bridge has been far from ideal, but he is delighted to be heading “home”.
He told the BBC: "It's not the way I wanted to leave, ever.
"I have special affection for the people at Chelsea. I'm not a person who is going to smear the image. They know the person I am."
Costa will not be freed to make his second debut for Atletico until January, as he waits for the next transfer window to officially open and for Atletico to finish serving a ban on registering new players.