The forward has recovered from a hamstring problem after undergoing horse placenta treatment in Belgrade, while Cristiano Ronaldo and Karim Benzema will play for Los Blancos
The Spain international appeared to have no chance of featuring in Lisbon after suffering a hamstring injury in last weekend's Liga title decider at Barcelona.
However, Costa travelled to Belgrade during the week to undergo a revolutionary treatment involving horse placenta and has now been given the all-clear to start up front alongside David Villa.
Ardan Turan, though, has lost his fitness race, with the Turkey international having succumbed to the hip issue that had been threatening his participation in the showpiece event.
Madrid, meanwhile, have been boosted by the availability of star striker Cristiano Ronaldo, who had been struggling with a thigh problem.
In addition, the Portugal international will be joined in Carlo Ancelotti's starting line-up by Karim Benzema, who has recovered from the hamstring injury that forced him off against Espanyol last weekend.
However, Pepe has been restricted to the role of substitute because of a calf strain, meaning Raphael Varane will start alongside Sergio Ramos at the heart of the Madrid defence.
Elsewhere, Sami Khedira, who only recently returned from a knee injury, takes over from the suspended Xavi Alonso in midfield.
Atletico Madrid: Courtois; Juanfran, Miranda, Godin, Filipe; Gabi, Tiago, Koke, Raul Garcia; Villa, Diego Costa.
Subs: Aranzubia, Alderweireld, Mario Suarez, Cristian Rodriguez, Sosa, Diego, Adrian Lopez.
Real Madrid: Casillas; Carvajal, Varane, Sergio Ramos, Coentrao; Khedira, Modric, Di Maria; Cristiano Ronaldo, Benzema, Bale.
Subs: Diego Lopez, Pepe, Marcelo, Arbeloa, Isco, Illarramendi, Morata.