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.
IOC president Thomas Bach said: “We have set the bar to the limit by establishing a number of very strict criteria which every Russian athlete will have to fulfil if he or she wants to participate in the Olympic Games Rio 2016.
Competitors from Russia who want to take part in the Games will have to meet strict criteria laid down by the IOC.
The Rio Games start on 5 August.