"President Putin has chosen a premeditated war that will bring a catastrophic loss of life and human suffering," Mr Biden said.
"The world will hold Russia accountable."
Mr Biden said that he planned to speak to his G-7 counterparts and would give a speech to the US people tomorrow.
He said he intended to announce "further consequences" that the US and its allies planned to impose on Russia over "this needless act of aggression against Ukraine and global peace and security."
"We will also coordinate with our NATO Allies to ensure a strong, united response that deters any aggression against the Alliance," Mr Biden said.
The UN Security Council held an emergency meeting today in New York that unfolded as Mr Putin's speech aired on Russian television and the explosions began in Ukraine.
Ukraine's Ambassador to the United Nations Volodymyr Yelchenko directly questioned Russia's representative in his speech.
"About 48 minutes ago, your president declared war on Ukraine," Mr Yelchenko said.
"You declared the war. It is the responsibility of this body to stop the war."
US Ambassador to the UN Linda Thomas-Greenfield spoke for a second time at the end of the UN meeting, stating Mr Putin had "delivered a message of war" while the Security Council was meeting.
She said the US would introduce a resolution in the UN tomorrow.
"At the exact time as we are gathered in the Council seeking peace, President Putin delivered a message of war in total disdain for the responsibility of this council," Ms Thomas-Greenfield said.