Media playback is not supported on this device
Wada says Ukad will take control of drug-testing in Russia as long as the Russian Anti-Doping Agency (Rusada) remains non-compliant with Wada's code.
Rusada was declared non-compliant in November following allegations it was involved in widespread doping.
Its athletes remain banned from international competition.
That suspension was imposed on 13 November after the publication of an independent Wada report that alleged "state-sponsored doping".
The ban will remain in place until Russia convinces athletics authorities it has sufficiently changed its practices.
Wada's statement said Ukad would be responsible for co-ordinating testing with the appropriate sport federations in the country.
It added: "Results management of all cases will be managed by a designated independent body, with full oversight by Wada."
UK Anti-Doping will provide "targeted and intelligence-led testing" on Russian athletes after signing a deal with the World Anti-Doping Agency.