Donald Trump has not reacted to Biden's decision so far.
He swept to victory on 5 November and will return to the White House on 20 January.
Trump has promised to end US involvement in foreign wars and use the taxpayers' money to improve the lives of Americans.
He has also said he will end the Ukraine war within 24 hours, but has not given details how.
Zelensky recently said he expected Trump to exert pressure on Ukraine and Russia to agree a peace deal within the next year.
Biden's decision was hailed by French President Emmanuel Macron as a "totally good" step.
The US authorisation could potentially enable France and the UK to grant Ukraine permission to use Storm Shadow missiles inside Russia. Storm Shadow is a Franco-British long-range cruise missile with similar capabilities to the ATACMS.
So far, neither Macron nor UK Prime Minister Sir Keir have publicly said whether they will allow Kyiv to use their missiles in the same way.
Meanwhile, China's Xi Jinping urged world leaders to “cool the Ukraine crisis” and seek a political solution, according to Chinese state media.
China has become a vital partner for Russia, as it seeks to soften the impact of US and European sanctions imposed over its full-scale invasion of Ukraine.
Beijing has repeatedly denied allegations that it supplies Moscow with weapons.