Sport's top court ruled there was "insufficient" evidence that the athletes had benefited from a system of state-sponsored doping at the last Winter Games, hosted by Russia.
CAS said in its judgement: "In 28 cases, the evidence collected was found to be insufficient to establish that an anti-doping rule violation (ADRV) was committed by the athletes concerned."
It added: "The evidence put forward by the IOC in relation to this matter did not have the same weight in each individual case."
The International Olympic Committee (IOC) has banned Russia from competing at Pyeongchang as a team over the doping scandal, although 169 Russian competitors have been cleared to take part as neutrals.
Forty-two Russians -- bobsleighers, cross-country skiers, competitors in the skeleton and ice hockey players -- appealed against the bans at CAS.
In addition to lifting the bans on the 28, CAS also lifted the life bans of another 11 Russians but barred them from competing at the Pyeongchang Olympics that start on February 9th.
Among those whose life bans were scrapped is Alexander Legkov, 34, who won gold in Sochi in the 50-kilometre freestyle cross-country skiing event and silver in the 4x10km relay, only to have his results annulled over the doping allegations.
Last week's extraordinary mass hearing of Russian athletes held less than three weeks before the Olympics begin forced CAS to temporarily move their compact headquarters in Lausanne to a large conference centre in Geneva.
The hearings at the world's top sports court were as a result of allegations of a vast state-sponsored doping programme contained in the report into Sochi authored by sports law professor Richard McLaren for the World Anti-Doping Agency.
His explosive findings laid out the workings of the programme, from the use of secret state agents to passing urine samples out of testing labs through mouseholes.
But for Russian deputy prime minister Vitaly Mutko, CAS's rulings proved Moscow never orchestrated a state-sponsored doping programme.
"One can say that there wasn't any system or any sort of manipulation at the Sochi Olympic Games, we've always said that but today the Court of Arbitration for Sport issued such a ruling," said Mutko, who himself is appealing to CAS over his life ban.
He was banned after being singled out in McLaren's report.
Many of the details about Russia's alleged state-supported doping programme were first uncovered by a groundbreaking German investigation.
Kremlin 'very glad'
News of Thursday's CAS verdict was warmly welcomed in Moscow.
"We are very glad for our athletes," President Vladimir Putin's spokesman Dmitry Peskov told reporters.
"The information about the decision of the Court of Arbitration for Sport proves that energetic work to stand up for our rights in court and elsewhere -- it is justified, it can be effective and it should continue," Peskov added.
"And we are hoping that this work will certainly continue."
He said it was unclear whether the 28 who had their appeals upheld would now compete in South Korea.
"It is a difficult question," the Kremlin spokesman added, noting Russian officials would continue talking to the IOC.
The IOC said on Thursday the lifting of the life bans did not "automatically" allow those athletes to compete at the Pyeongchang Games.
"Not to be banned does not automatically confer the privilege of an invitation" to the 2018 Games in South Korea, the IOC explained in a statement.
Those Russians already cleared to take part in the Games will do so under the designation 'Olympic Athlete from Russia'.