Perkins, 30, announced he was switching allegiance to Russia earlier this year after failing to get on Australia's track cycling team for the 2016 Rio Olympic Games.
A decree published by the Kremlin said Putin had signed off on granting the rider -- who is currently in Saint Petersburg for Russia's national championships -- citizenship.
The rare defection by an Australian athlete raised eyebrows since Melbourne-born Perkins has no family ties to Russia.
Perkins won bronze in the individual sprint at the London Olympics in 2012 after claiming first place at the 2011 World Championships in the keirin event.
His switch to Russia comes at a time when the country is in the spotlight after an alleged state-sponsored doping system was uncovered.