In a decision issued on Thursday, the Court for Arbitration for Sport (CAS) said it "unanimously found" that the evidence presented against 28 athletes were "found to be insufficient to establish" that doping rules were violated.
"We are very glad for our athletes", said President Vladimir Putin's spokesperson Dmitry Peskov.
The sanctions against them were annulled and their individual results achieved in Sochi 2014 were reinstated.
The result of the CAS decision does not mean that athletes from the group of 28 will be invited to the Games, the International Olympic Committee said in a separate statement later on Thursday.
The IOC has banned Russia from competing at Pyeongchang as a national team over the doping scandal, although 169 Russian competitors have been cleared to take part as neutrals. A hearing for the remaining three athletes was postponed.
"There wasn't any system or any sort of manipulation at the Sochi Olympic Games", Vitaly Mutko told the meeting chaired by prime minister Dmitry Medvedev.
Along with the ban, Russian Federation was fined $15 million in December after athletes were found doping in major global competitions, most notably in the 2014 Sochi Olympic and Paralympic Games.
"This, of course, can not but give us joy", he said.
Court of Arbitration for Sport overturns doping bans on Russian athletes
"I think that the least the International Olympic Committee could do is allow them to participate", Philippe Baertsch, a lawyer for the athletes, told The Associated Press.
On Thursday, the Court of Arbitration for Sport (CAS) based in Lausanne, Switzerland announced that 28 Russian athletes that were banned for life by the International Olympic Committee (IOC) late past year, following an investigation into allegations of doping violations that emerged after the 2014 Winter Olympics held in Sochi, would be lifted.
Kolobkov says "the criteria for not allowing in our athletes. were based on criteria which partly intersect with the conclusions" challenged in the appeal cases, "so this raises a lot of legal questions".
"I'm partly satisfied with the CAS decision because we had a large number of athletes who were exonerated - all the skeleton athletes and some of the bobsledders.We would like to see what is said about the athletes who were not fully exonerated". It expressed its "satisfaction on one hand and disappointment on the other" at Thursday's decision, made eight days before the 2018 Winter Olympics begin in South Korea.
A further 11 Russians lost their appeals, which the International Olympic Committee says "clearly demonstrates once more the existence of the systemic manipulation" of the Sochi anti-doping system. The committee released the detailed information the panel used in the review who out of "the pool of 389 athletes...could potentially be invited to the games depending on available quota places".
Cross-country skier Alexander Legkov, who won gold in the 50km and silver in 4x10km, and Alexander Tretyakov, who won gold in the men's individual skeleton, were among those to be cleared.
In reaching its decision, Cas said it considered testimony from experts including former Russian anti-doping official and whistleblower Dr Grigory Rodchenkov and Canadian lawyer Professor Richard McLaren, who authored a damning 2016 report into doping in Russia.
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