The 33-year-old, who turns 34 on October 7, completed his medical and signed as a Wolves player late last week but his official unveiling was delayed due to the death of Queen Elizabeth II.
Now, Wolves have announced that the striker has completed a one-year deal at the club. There is no option for a second year.
Costa's move to Molineux was originally under threat after he failed to automatically qualify for a work permit but a three-person panel granted him a permit after Wolves appealed. He flew into England on Wednesday and had his medical on Thursday.
The former Spain international arrives at Wolves as arguably one of their biggest-name signings in their history. He scored 59 goals during a three-year stay at Chelsea between 2014 and 2017, where he won the Premier League twice and had a distinguished career at the top of the game.
He moves back to the Premier League after a spell with Brazilian outfit Atletico Mineiro, who he terminated his contract with in January. Costa last played for them on December 5.
Wolves acted fast to bring the free agent to Molineux after £15.4million summer acquisition Sasa Kalajdzic suffered an anterior cruciate ligament injury on his Wolves debut against Southampton last weekend. He will now provide competition for Raul Jimenez, with Wolves struggling for goals.
Wolves chairman Jeff Shi said: “We are absolutely delighted to welcome Diego Costa to Wolves, and back to the Premier League.
“A serial winner with a wealth of experience at the highest level, Diego will bring something unique to our dressing room and on the pitch, and we look forward to his impact at Molineux and Compton this season.”