Austrian striker Sasa Kalajdzic, Wolves' new 18 million euros ($18.24 million) recruit, sustained a knee ligament injury on his debut while Mexico forward Raul Jimenez was sidelined with a groin injury.
Costa, 33, was a free agent after leaving Brazilian side Atletico Mineiro in January and after passing a medical last week he has signed a one-year deal with Wolves, subject to international clearance.