The 33-year old had been without a club since January after terminating his contract with Brazilian side Atletico Miniero at the start of the year and now the former Spain international is set for a free agent return to English football with Wolves.
Bruno Lage is keen on Costa's services after new signing Sasa Kalajdzic suffered an ACL injury at the weekend.
The forward, signed from Stuttgart for £15.4million the day before deadline day, picked up the injury during his side's victory over Southampton at the weekend and the Austrian is expected to be out of action for some time as a result.
Brazilian-born Costa will join a cohort of Portuguese players at the Midlands club in the hope he can help Wolves up the table towards the European spots which the club came so close to last season, as they finished five points off a Europa Conference League qualification place.
With Raul Jimenez experiencing injury troubles of his own, Costa could prove to be a very astute signing, with his time at Chelsea proving he is one of the most feared strikers the Premier League has seen.
Costa scored 52 league goals for Chelsea in four years at the club, hitting 20 goals in both seasons that Chelsea won the league (2014/15 and 2016/17).
The striker left SW6 under a cloud in January 2018, when at the end of the 16/17 season, then Blues boss Antonio Conte broke the news to Costa that he was no longer part of his plans via text, and the forward was subsequently sold back to Atletico Madrid for £57million.
It is unclear how long the striker will be at Wolves upon his arrival, but if he hits the ground running at Molineux, fans across the country will hopefully be treated to some prime Costa performances which bought them so much joy during his successful spell in England.
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