Diego Costa will have his Wolves medical on Thursday after having his visa granted by the Football Association upon appeal.
The former Chelsea and Atletico Madrid forward, 33, has agreed a deal until next summer after signing as an out-of-contract player.
Costa was initially denied a work permit because he did not fulfill the points criteria.
He last played for Brazilian side Atletico Mineiro in January.
Wolves had made a special application, which has now been approved.
Costa is due to fly into England on Wednesday evening before completing his move to join Bruno Lage's side.
With Raul Jimenez and new signing Sasa Kalajdzic set to miss Saturday's Premier League trip to Liverpool through injury, Wolves could be without a recognised striker at Anfield.
It remains to be seen whether Lage picks Costa in his squad after so long out.
Wolves play Manchester City at Molineux immediately before the international break on Saturday, 17 September.
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