24-year-old Grbic has reportedly joined the La Liga giants for an initial €4m plus €2m in potential bonuses.
24sata says the clubs had been negotiating for several days and that Grbic has already signed a four-year deal with Atleti.
Although he has signed an agreement, until he travels to Madrid for a medical the deal cannot be made official.
However, Lokomotiva were able to get permission from Atleti to play Grbic in at least two European games.
The Zagreb club reached the Champions League qualifiers last season, with Grbic’s performances instrumental in that.
6’5″ tall Grbic will replace Antonio Adan as Atletico’s number two with the 33-year-old about to join Sporting CP.
The club’s number one is Jan Oblak, considered by many to be the best goalkeeper in the world.