"Putin expressed hope for joint work to restore Russian-American relations from their state of crisis, and also to address pressing international issues and search for effective responses to challenges concerning global security," the Kremlin said in a statement.
Putin also said he was sure a constructive dialogue between Moscow and Washington would serve the interests of both countries, the Kremlin said.
Earlier the leader of Russia's nationalist Liberal Democratic party, Vladimir Zhirinovsky, welcomed Trump's win.
According to the Interfax news agency, Zhirinovsky said: "We of course regard with satisfaction that the better candidate of the two presented to the American voters was victorious."
He also said that he hopes the Trump victory means that US Ambassador John Tefft departs.
He says, "We hope that this ambassador leaves Russia ... he hates Russia."
Kirill Dmitriev, the head of Russia's sovereign wealth fund, said on Wednesday he Trump's presidential victory would reduce geopolitical confrontations.
"A less confrontational US foreign policy will unlock major opportunities for joint (Russia-US) trade and investment," Dmitriev, head of the Russian Direct Investment Fund, said in a statement.
Dmitriev said he believed financial markets would recover quickly "just as they did after the Brexit vote."
