The IOC barred the entire Russian Olympic team from the Games that concluded in South Korea on Sunday after investigations into state-sponsored doping.
"I would like to thank our athletes who were able to perform well even despite the provocations", Russian Olympic Committee President Alexander Zhukov said in televised remarks.
Three days after the closing ceremony, the International Olympic Committee lifted Russia's suspension from the movement because "only" two of their 168 athletes deemed "clean" enough to compete anyway failed drug tests.
'The final notification of all remaining test results from the Olympic Athlete from Russia (OAR) delegation has been received from the Doping-Free Sport Unit (DFSU),' the IOC said in a statement.
Russian officials and others had expressed hopes that the ban could be lifted before the closing ceremonies.
Russian Federation has still not acknowledged there was a state-controlled doping operation in the country, something described in great detail by its former doping laboratory head Grigory Rodchenkov and confirmed by three separate investigations.More news: ZTE launches Android Go smartphone for United States market
Two of that number failed drug tests but the IOC has still chosen to reinstate Russia's Olympic membership, provoking anger among the worldwide sporting community. They all competed as Olympic Athletes from Russian Federation at PyeongChang.
The country's Olympic committee paid some $15 million in fines.
"For us today's decision by the International Olympic Committee is very important". The World Anti-Doping Agency said it would continue to regard Russia's domestic drug testing organization as noncompliant until it does.
Russian Federation won two golds, six silvers and nine bronzes in the PyeongChang Olympics.
"The Russian Olympic Committee has had its rights fully restored", he said.
Russian athletes were not allowed to compete under their national flag at this month's games and instead formed the "Olympic athlete from Russia" team.