Russia will have "the cleanest team" at Rio 2016, claims the country's Olympic Committee president Alexander Zhukov, Censor.NET reports citing BBC.
Five athletes - three track cyclists, a wrestler and a canoeist - are still waiting to hear if they can take part. The final number will be revealed on Friday, Zhukov said.
The International Olympic Committee (IOC) asked individual federations to decide whether Russians could compete after an independently commissioned report found evidence of a four-year, state-run "doping programme".
A three-person IOC panel has ratified 18 shooters, 11 boxers, 11 judokas, eight tennis players, six sailors, five equestrian riders, three archers and one golfer, among others,
Russian news agency R-Sport said 29 swimmers and canoeing world champion Andrey Kraitor were also free to compete at the Games.
The International Weightlifting Federation excluded all eight Russians entered for Rio last week and the Court of Arbitration for Sport (Cas) ruled the ban had been "properly applied".
Appeals by 17 Russian rowers were also rejected at the hearing in Brazil.
Cas has now heard 18 cases since its division in Rio was opened on 26 July, a record for one Olympics.
The Cas panel ruled that the International Rowing Federation (Fisa)'s decision to deny the rowers entry to the Rio Games was in accordance with the IOC decision of 24 July, which set out the criteria for the admission of Russian athletes to compete in Brazil.
Meanwhile, Russia's Pavel Sozykin has had his doping ban overturned by World Sailing and his case will also now be heard by the three-person IOC panel, which is making the final decision on all of the country's athletes in Rio.
Any Russian who has served a doping ban will not be eligible for the Olympics. Track and field athletes have already been banned.