Last year, an independent report commissioned by Wada found evidence of state-sponsored doping in the country.
Wada told Russia earlier this month the "best solution" is to "work with them" following new intelligence.
Kuwait, Equatorial Guinea and Mauritius were also found non-compliant.
Wada has 'new Russia doping intelligence'
Russia's anti-doping agency (Rusada) has been suspended since an initial Wada report in 2015, but the country's authorities deny there was a state-backed programme.
Rusada has pledged to follow international recommendations to get the suspension lifted, with the International Olympic Committee (IOC) making the ultimate decision on the country's participation in the Winter Games.
The IOC has said it will make its decision at its next board meeting, which takes place from 5-7 December.
The Games take place from 9-25 February in South Korea.
What was Russia's reaction?
Russian Sports Minister Pavel Kolobkov said the criteria for reinstatement have a "political character".
"I got the impression that the decision was made in advance," told TASS news agency after Wada's announcement, which was made on the recommendation of its independent compliance review committee.
"We believe that the state has fulfilled all of its obligations."
In September, Russian Olympic Committee president Alexander Zhukov said he expected the country to have a team at the Pyeongchang Games.
Why were Russian athletes banned?
Russia was suspended from track and field events by the International Association of Athletics Federations in November 2015 following the publication of the independent Wada report.
Sports minister Vitaly Mutko apologised for Russia's failure to catch the cheats, but stopped short of admitting the scandal had been state-sponsored.
However, an independent report commissioned by Wada and completed by Canadian law professor Richard McLaren contained more damaging allegations and suggested senior figures in Russia's sports ministry were complicit in an organised cover-up.
The report implicated the majority of Olympic sports in the cover-up and claimed Russian secret service agents were involved in swapping positive urine samples for clean ones.
As a result, Wada recommended all Russian athletes be banned from competing in the Rio 2016 Olympic Games.
But the IOC chose not to impose a blanket ban, instead leaving decisions on whether Russians could compete to individual sporting federations.
In total, 271 Russians competed in Rio.
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