The International Olympic Committee (IOC) will leave it up to individual sports' governing bodies to decide if Russian competitors are clean and should be allowed to take part.
The decision follows a report in which Canadian law professor Richard McLaren said Russia operated a state-sponsored doping programme from 2011 to 2015.
The Rio Games start on August 5th.
Competitors from Russia who want to take part in the Games will have to meet strict criteria laid down by the IOC.
Any Russian athlete who has served a doping ban will not be eligible for next month's Olympics.
