Putin, who was president from 2000 to 2008 before becoming prime minister due to term limits, won more than 63 percent of Sunday's vote.
The opposition and independent observers said the election was marred by massive fraud, including "carousel voting," in which busloads of voters are driven around to cast ballots multiple times.
Putin on Tuesday shrugged off opposition allegations of rampant vote fraud as irrelevant. "It's an element of political struggle, it has no relation to the election," he said.
His campaign has been laced with anti-Americanism, including claims that the United States had instigated the opposition protests in order to weaken Russia. The strident rhetoric resonated well with his support base of blue-collar workers, farmers and state employees.
He can be expected to continue the same tough policies he has pursued as prime minister, including opposing U.S. plans to build a missile shield in Europe and resisting international military intervention in Syria.
Russia's foreign ministry on Tuesday dealt a blow to Western hopes that Moscow might drop its support for Syrian President Bashar Assad after Putin's election, saying firmly that it sees no reason to change its stance.
"We are deeply convinced that we are right," Deputy Foreign Minister Sergei Ryabkov told reporters. "That is why we call on our partners not to adopt a hard-line stance, but to seek compromise, stimulate negotiations and a political process."
The ministry dismissed hopes for a change in the Russian position on Syria as "wishful thinking."
"Russia's stance on the Syrian settlement has never been subject to any short-term considerations and hasn't formed under the influence of electoral cycles, unlike that of some of our Western colleagues," it said.
Russia has protected Assad from U.N. sanctions over his crackdown on protests and accused the West of fueling the conflict by backing the Syrian opposition.
Moscow has warned it would block any U.N. resolution that could pave the way for a replay of what happened in Libya, where NATO action helped oust dictator Moammar Gadhafi.