The Court of Arbitration for Sport will settle the dispute over Russian athletes' participation at the Rio Olympics on July 21.
Sixty-eight competitors are opposing the IAAF ban of all Russian track and field athletes following widespread doping allegations, with the athletes saying they are being punished despite having competed without doping.
On Friday, Russia's 800m runner Yulia Stepanova was given permission to compete in Rio as a neutral athlete after being granted an exemption from the ban by the IAAF because she had "made a truly exceptional contribution to the protection and promotion of clean athletes, fair play and the integrity and authenticity of the sport".
More than 80 athletes have applied for the same exemption to compete under a neutral flag and must get evidence that they have been the subject of reliable drug-testing outside Russia to the IAAF two weeks before the Olympics.
CAS said on Monday the Russian Olympic Committee (ROC), the IAAF and the Russian athletes had all agreed to the body making the decision ahead of the Games, which start on August 5.
The 68, chosen by the suspended Russian track federation, were "of absolutely flawless reputation, not involved in doping scandals, not linked to certain coaches," according to Russia's legal head, Alexandra Brilliantova.
The parties have agreed to an expedited procedure which should conclude on July 21 2016 with the issuance of the final decision," CAS said in a statement.
Meanwhile, the Russian Rowing Federation plans to appeal to CAS to contest a doping ban barring its men's quadruple sculls crew from the Rio Olympics.
One of the crew members, Sergei Fedorovtsev, provided a urine sample at an out-of-competition test conducted by the Russian Anti-Doping Agency on May 17 and tested positive for the prohibited substance trimetazidine.