The Spanish forward was initially denied a permit to play in England but Wolves appealed the decision and a panel have now granted the 33-year-old permission to arrive in the West Midlands to complete his Molineux switch.
Costa was identified as Bruno Lage's candidate to provide competition up front after it was revealed new boy Sasa Kalajdzic sustained an ACL injury on his debut against Southampton last weekend.
He will now undergo a medical at Compton Park with the view to signing a one-year deal at Molineux.
Costa, 33, scored 52 goals in 89 appearances for Chelsea between 2014 and 2017 but has seen only limited playing time after leaving Madrid in late 2020.
The former Spain international has been a free agent since January when he terminated his contract at Brazilian club Atletico Mineiro.
The three-person work permit panel took into account the experience and value of the player, meaning Wolves have benefitted from Costa’s impressive career to date.
Wolves also proved ‘exceptional circumstances’ that prevented Costa picking up 15 necessary points in order to automatically qualifying for the original permit.
Costa could be registered in time to be available for Wolves' trip to Liverpool at the weekend although it will take time for Costa to build up his match-fitness.
The striker is set for an emotional return to Chelsea when Bruno Lage's men travel to Stamford Bridge on October 8.