The announcement of the meeting was made Thursday by the Russian president's spokesman Dmitry Peskov and confirmed by the White House.
Putin is to speak Monday at the United Nations General Assembly. It was not immediately clear if the meeting with the U.S. President would take place before or after the speech. Peskov said Putin also is to meet Japanese Prime Minister Shinzo Abe on Monday.
U.S.-Russian relations deteriorated significantly after Russia annexed Crimea from Ukraine more than a year ago. The United States, as well as other Western countries, imposed sanctions on Russia over the annexation and over claims that Russia is supporting an insurgency in eastern Ukraine with troops and arms.
Russia vehemently denies it is militarily involved in eastern Ukraine and portrays the sanctions and strong criticism from the United States as attempts to undermine the country and force Putin from power.
Russia, meanwhile, is ramping up its involvement in the Syria conflict. It recently has ferried weapons, troops and supplies to an airport near the Syrian coastal city of Latakia in what the U.S. sees as preparations for setting up an air base there.
Moscow has denied that it is building up its presence there in order to protect its longtime ally, Syrian President Bashar Assad, but said instead that it wants to help him fight the Islamic State group.
The last time Putin and Obama were face to face was a series of brief encounters last November at the Asia-Pacific Economic Cooperation summit in Beijing. They have spoken by telephone three times since then.
The White House said Monday's meeting was arranged at Putin's request and that despite deep differences with Moscow, Obama felt it would be irresponsible not to assess whether progress could be made on the Ukraine and Syria crises.
This story has been corrected to show that last year's APEC summit was in Beijing, not Berlin.