The two leaders will speak by phone on Thursday.
They will discuss forthcoming security talks between the countries and the situation in Europe, a White House official said.
Russia, which recently built up forces on the border with Ukraine, denies planning to invade the country.
It says its troops are there for exercises, and that it is entitled to move its troops freely on its own soil.
Hours before the call, Mr Putin told Mr Biden in a holiday message he was “convinced” the pair could work together based on “mutual respect and consideration of each other’s national interests”.
His spokesman, Dmitry Peskov, said Moscow was “in the mood for a conversation”.
A day earlier, a US official told AFP news agency that Mr Biden would offer his Russian counterpart a “diplomatic path” but remained “gravely” concerned by the Russian troop build-up on the border.
The head of Ukraine’s national security council, Oleksiy Danilov, sought to downplay that on Thursday, saying: “As for the troops build-up near our borders reported by foreign media – we do not see that. There is a certain increase of [Russian] military and we closely monitor what’s happening at our borders.”
Less than a month ago, Ukraine’s defence minister told parliament – citing intelligence reports – that Russia had massed more than 94,000 troops near the border and could be gearing up for a large-scale military offensive at the end of January.
The US has consulted European leaders ahead of the call to co-ordinate a common response to the Ukraine issue, according to a White House statement.
While Ukraine is not a Nato member, it has close ties with the bloc.
Russia has said it wants legally binding guarantees that Nato will not move eastwards and that weapons will not be sent to Ukraine or any neighbouring countries.
Nato Secretary-General Jens Stoltenberg has been adamant that Ukraine’s membership of the alliance is a matter for Nato and Kyiv. “Any dialogue with Russia has of course to respect the core principles which European security has been based on,” he previously said.
Lithuanian President Gitanas Nauseda has described the current situation as probably “the most dangerous it’s been in 30 years”.
Russian officials are due to meet US counterparts in Geneva on 10 January. Asked earlier this week if he would meet Mr Putin on that date, Mr Biden replied “We’ll see”, but he is not expected to attend the talks in Geneva.