The action effectively enforces EU sanction because the world's financial transactions are impossible without using SWIFT, and it will go a long way toward isolating Iran financially.
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The company's name stands for Society for Worldwide Interbank Financial Telecommunication. It is a banking hub crucial to oil, financial transactions and other trades.
In a statement, SWIFT said the EU decision "prohibits companies such as SWIFT to continue to provide specialized financial messaging services to EU-sanctioned banks."
"Disconnecting banks is an extraordinary and unprecedented step for SWIFT," Lazaro Campos, chief executive of SWIFT, said. "It is a direct result of international and multilateral action to intensify financial sanctions against Iran."
In addition to sanctioning various officials and freezing the assets of certain companies, the European Union plans to institute an embargo on the import of Iranian oil in July an attempt to choke off funding for Iran's nuclear program.
'Intransigence has a price'
The EU sanctions are aimed at forcing Iran to demonstrate to the international community that it is not trying to develop nuclear weapons. Iran says that its nuclear program is for peaceful purposes only, but officials in many other countries including Israel believe otherwise.
Prime Minister Benjamin Netanyahu welcomed SWIFT global financial transaction service's decision to cut its ties with Iranian banks.
The White House also welcomed the move, saying it was part of the growing sanctions on Iran and its global isolation.
White House Spokesman Jay Carney said Thursday that SWIFT's decision "is part of a process of tightening sanctions.
"It is part of the process of isolating Iran and making clear to the Iranian leadership that there is a price to pay for their intransigence, their refusal to abide by their international obligations, their refusal to adequately reassure the international community that its nuclear intentions are peaceful and non-weapon-related," he said.
The United States, he added, has "made clear, as we did earlier this year, that when it was the case that we had already implemented the harshest sanctions with the broadest international coalition in history, that we were going to continue to ratchet them up. And this is certainly – as part of the international effort, this is part of it."
Attila Somfalvi and Yitzhak Benhorin in Washington contributed to this report