Wada's independent commission examined allegations of doping, cover-ups, and extortion in Russian athletics, which also implicated the IAAF, the sport's world governing body.
It says London 2012 was "sabotaged" by "widespread inaction" against athletes with suspicious doping profiles.
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Russia was also accused of running a "state-supported" doping programme.
The report recommended that five athletes and five coaches should be given lifetime doping bans.
IAAF president Lord Coe told the BBC that the Russian athletics federation, Araf, had been asked to respond to the allegations by the end of the week. The 59-year-old said that after reviewing the feedback the IAAF "would look at a range of options, including sanctions", which could result in suspension from the sport.
"I'm not putting in a time frame but I will do whatever is necessary. This is not a swift road back," he added.
The commission's chairman, Dick Pound, who led a Wada news conference on Monday, also recommended that the Russian federation is banned from next year's Olympics.
"One of our hopes is they will volunteer to take the remedial work," he said. "If they don't the outcome may be no Russian track and field athletes in Rio. I hope they recognise it is time to change."
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Russia's sports minister Vitaly Mutko told Interfax news agency that recommendations made on the basis of the report would be fulfilled, while the acting head of Araf Vadim Zelechenok said it was not for Wada to call for suspensions.
He also told the R-Sport TV station: "Any suspension should be discussed at the meeting of the IAAF in November. It should be proven that any violations were the fault of the federation and not individual sports people. We should be given a chance to clear our names."
The international police body Interpol says it will be co-ordinating a global investigation into the suspected corruption and doping.
The report's co-author, sports lawyer Richard McLaren, believes it shows "a different scale of corruption", even compared with football's ongoing Fifa scandal, saying actual results at international athletics competitions had been changed because of cheating.
The report also:
The report was commissioned on a "very narrow mandate" to "determine the accuracy" of allegations made in a German TV documentary about Russian athletics last December.
It claimed Russian athletes paid 5% of their earnings to domestic doping officials to supply banned substances and cover-up tests, while athletics' world governing body the IAAF was implicated in covering up the abuse.
The programme's claims of widespread doping were made by former Russian Anti-Doping Agency (Rusada) official Vitaly Stepanov and his wife Yulia (nee Rusanova), formerly an 800m runner who was banned for doping.
It included testimony from Russian athletes admitting to using banned substances and evidence of doping and corruption.
Separate doping claims were made in August when The Sunday Times and a German broadcaster claimed that leaked blood tests from 5,000 athletes over 11 years showed an "extraordinary extent of cheating". The IAAF said the allegations were "sensationalist and infuriating" and the commission's remit was widened to include them. It will report back on those claims later in the year, Pound said.
IAAF chief Lord Coe said the sport's governing body would wait for Russia's response before deciding whether to punish the country's federation.
"It is the right thing to do to get them to give us an answer," he told the BBC.
"I am responsible for the conduct of my sport and I want answers from the Russian athletics federation. I am tough enough to defend my sport but the point I would emphasise is this is not just limited to athletics or Russia.
"We clearly have to understand full scope of allegations. We will look at ourselves. We will move quickly on this. I want to see a sport which is transparent and accountable and I will do what I can to do that. It will not be a swift road."
BBC 5 live Track & Field special - Including former athletes Steve Cram, Paula Radcliffe and Darren Campbell examining the independent report on claims of corruption and cover-ups in world athletics.
Russia should be banned from athletics competition, a World Anti-Doping Agency commission report has recommended.