The announcement came three days after Russian flagship carrier Aeroflot said it would restart flights between the two capitals from April 11.
EgyptAir flights are set to resume the following day.
Both companies suspended the route in October 2015 after an airliner operated by Russia's Kogalymavia, carrying holidaymakers from the south Sinai resort of Sharm El-Sheikh, crashed, killing all 224 people on board.
The Egyptian branch of the Islamic State group claimed the attack.
Safwat Musallam, head of EgyptAir Holding, said on Friday the carrier planned to operate three Cairo-Moscow flights a week.
Aeroflot is planning the same number of flights but will run extra services during the football World Cup, to be held in Russia from June 14 to July 15.
The Russian airline said on Tuesday that Egypt had met its demands for stricter security measures.
Prior to the attack, Egypt vied with Turkey as the most popular destination for Russian tourists.
But the 2015 attack dealt a heavy blow to Egypt's tourism sector, already suffering from low visitor numbers in the wake of the 2011 revolt that toppled longtime president Hosni Mubarak.
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