Speaking in parliament, Starmer told Abramovich: "Honour the commitment you made and pay up now, and if you don't, we are prepared to go to court so every penny reaches those whose lives have been torn apart by Putin's illegal war."
Ministers in June said they were "frustrated" by the failure to reach an agreement with Abramovich over where the funds of the May 2022 sale should go.
The UK government wants the funds to be directed towards humanitarian purposes in Ukraine, but the oligarch insists they be used for all victims of the conflict, including in Russia.
A consortium led by US businessman Todd Boehly bought the Premier League giants after Abramovich was sanctioned following Russian President Vladimir Putin's invasion of Ukraine.
The frozen funds are being held in a UK bank account.
They still legally belong to Abramovich and cannot be moved without a licence from the Office of Financial Sanctions Implementation.
But Starmer told lawmakers Wednesday that the government was now issuing such a licence.
"I can announce that we're issuing a licence to transfer £2.5 billion from the sale of Chelsea Football Club that's been frozen... since 2022," he said.
"My message to Abramovich is this: the clock is ticking," the prime minister added.
The 59-year-old Russian-Israeli billionaire bought the club in 2003 and had an estimated fortune of $14.5 billion in 2021.
Chelsea enjoyed their most successful ever period under Abramovich, winning two Champions Leagues, five Premier Leagues, five FA Cups, two Europa Leagues and a Club World Cup.