Australia was joined in the referral to the ICC by allies such as the UK, US, New Zealand, Canada and European partners.
The referral was the largest in the history of the International Criminal Court.
The court's prosecutor Karim Khan said the investigation had begun following the referral.
"I have notified the ICC presidency a few moments ago of my decision to immediately proceed with active investigations in the situation," he said in a statement.
"Our work in the collection of evidence has now commenced."
Mr Khan said on February 28 the prosecutor's office had already found a "reasonable basis" that war crimes had been committed during Russia's invasion of Ukraine.
Australia also joined other nations in opposing Russian aggression in Ukraine during an emergency session of the UN General Assembly.
There were 141 nations in favour of condemning Russia's actions, while five voted against, including Russia, North Korea and Syria.
A further 35 members of the UN abstained from the vote, among them China and India.
Australia's ambassador to the United Nations Mitch Fifield said Australia was firmly alongside other nations in support of Ukraine.
"We've chosen to stand with Ukraine and work against the scourge of war," he said.
"President Zelenskyy and the people of Ukraine, today, we have sent you the strongest sign we are with you, we've shown we will not let you go."
An Australian air force flight carrying critical military equipment and medical supplies has left Richmond RAAF base for Europe.
Australia had pledged $70 million in lethal and non-lethal military aid to Ukraine following the Russian invasion.
Prime Minister Scott Morrison said the support would include missiles and ammunition, however, the exact amount would not be specified due to national security concerns.
Home Affairs Minister Karen Andrews said the exact number of people to be accepted from Ukraine on refugee visas was not yet decided.
Ms Andrews said Australia was providing humanitarian assistance to people fleeing Ukraine but she expected the majority of people who evacuated to neighbouring countries would seek to return to Ukraine as soon as possible.
"We've certainly stepped up and made sure that we are processing the visa applications that are coming through," she told Sky News on Thursday.
"These people are most likely going to want to return home - families have been separated - so there's these issues with how we would manage that."
