"The great majority of Wada's executive committee decided to reinstate Rusada as compliant with the world anti-doping code subject to strict conditions," said Wada president Craig Reedie.
The Russian government hailed the move. Olga Golodets, a deputy prime minister, told Russian news agencies that the country's authorities had worked hard to improve testing.
"We welcome Wada's decision," she added. "Over the past years Russia has done enormous work to create transparent and understandable measures to prevent doping. Russia confirms its adherence to the principles of clean sports competition."
The extent of Russian state involvement in doping was revealed in 2015 when Grigory Rodchenkov exposed the networks between athletes and the secret services.
Jim Walden, the lawyer representing Rodchenkov, said on Thursday. "Wada's decision to reinstate Russia represents the greatest treachery against clean athletes in Olympic history."
The softening of Wada's stance has triggered outrage from athletes and national anti-doping agencies. They have accused Wada of caving in to pressure from the International Olympic Committee.
However, outling the conditions for the return to the fold, Reedie added: "This decision provides a clear timeline by which Wada must be given access to the former Moscow laboratory data and samples with a clear commitment by the executive committee that should this timeline not be met, it would support the compliance review committee's recommendation to reinstate non-compliance."