Aljazeera's correspondent in Moscow said Russia would also release two Qataris it detained in Moscow on Saturday.
Speaking on Sunday evening, Aljazeera's Akram Khuzam said the releases would happen "in the coming hours".
It is thought they will help to ease a diplomatic spat which has strained relations between the two countries.
Salim Khan Yandarbiyev, a Chechen separatist, was killed in the Qatari capital on 13 February after his booby-trapped car exploded outside a mosque.
Two of Yanderbiyev's bodyguards were also killed in the explosion, and his 13 year-old son was seriously wounded.
Qatar arrested three Russian security agents the following week as part of its investigation into the killings, but promptly released one of them.
Yanderbiyev's car was blown up
after Friday prayers
Russia reacted with outrage to the arrests, denied all involvement in the deaths and pressed Doha to release its nationals.
Then on Saturday, Russia detained two Qataris thought to be part of a judo team in transit in Moscow in what was widely seen as a tit-for-tat gesture.
Qatar's mainly government-owned Asharq newspaper immediately ran an editorial headlined "Russian-style piracy", and charged Moscow with "jungle diplomacy".
The leading daily accused Moscow of seeking to use the men "to barter" for the two security agents it had charged.