Shakhtar seal Costa signing
Costa, 19, has signed a five-year deal.
Shakhtar, who boast a host of Brazilian talent in their squad, face England's Fulham in the Europa League last 32 tie next month.
The youngster was widely tipped to complete a move to the Premier League during the close-season, with both the Red Devils and Gunners linked with Costa's signature.
Reports claimed Sir Alex Ferguson had hoped to bring the Samba sensation to Old Trafford to support Wayne Rooney and Dimitar Berbatov in attack following the losses of Cristiano Ronaldo and Carlos Tevez.
While Emirates Stadium supremo Arsene Wenger was put under pressure from his own supporters to add to his squad during the close-season - calls that have been vindicated following the absence through injury to Robin van Persie, Nicklas Bendtner and Eduardo, meaning Russian playmaker Andrei Arshavin has been converted into a makeshift front-man.