Moscow has not revealed any losses in the conflict since its first weeks, but Western officials and the Kyiv government say they number in the thousands.
The increase includes a 137,000 boost in the number of combat personnel to 1.15 million. It comes into effect on January 1, according to the decree published on the government's legislative portal.
The last time Putin fixed the size of the Russian army was in November 2017, when the number of combat personnel was set at 1.01 million from a total armed forces headcount, including non-combatants, of 1.9 million.
Russian and Ukrainian armed forces
Russia has not said how many casualties it has suffered in Ukraine since the first weeks of the campaign when it said 1,351 of its soldiers had been killed.
Western estimates say the actual number could be at least 10 times that, while Ukraine says it has killed or wounded at least 45,000 Russian troops since the conflict - which Moscow calls a special military operation - started on Feb. 24.
Kyiv has also been reluctant to publish information on how many of its soldiers have died in the war, but on Monday the head of Ukraine's armed forces said almost 9,000 service personnel had been killed in a rare update.
Putin's decree did not say how the increase in headcount was to be achieved but instructed the government to assign the corresponding budget.
According to an authoritative annual report by the International Institute for Strategic Studies, Russia had 900,000 active service personnel at the start of this year, and reserves of 2 million people with service within the past five years.