Berlin had been one of the few countries opposing action after Britain, the European Union, Canada and the United States all pressed the case as part of their package of sanctions against Vladimir Putin and the Kremlin.
“As Russian forces unleash their assault on Kyiv and other Ukrainian cities, we are resolved to continue imposing costs on Russia that will further isolate Russia from the international financial system and our economies,” Western allies said in a joint statement.
Such a move deals a blow to Russian trade by making it more difficult for its companies to do business around the world.
Swift has been used as a weapon in the past when Iranian banks were kicked out of the banking system, as part of a wider package of measures against Tehran that prompted a steep economic downturn.
Western allies also said they would limit the ability of wealthy Russians to buy citizenship in other countries.
“Specifically, we commit to taking measures to limit the sale of citizenship—so called golden passports—that let wealthy Russians connected to the Russian government become citizens of our countries and gain access to our financial systems,” they said.
But the Telegraph understands that figures in the UK and some European countries are concerned that removing Russia from Swift could present a “security risk” to the West.
There are concerns about potential Kremlin-ordered cyber attacks on Swift if Russia no longer has “skin in the game”, as well as the potential for Moscow and Beijing to build a rival payment system without any involvement from western countries.
A Whitehall source said: “There are a lot of consequences of pushing the Russians off a financial system that would mean them potentially building their own.” Governments needed to consider “what behaviour and actions are precipitated by removing them from it”, the source added.
In other developments on Saturday, French authorities seized a ship in the English Channel suspected of belonging to a Russian company targeted by European Union sanctions over the war in Ukraine.
The cargo vessel transporting cars to St Petersburg was “strongly suspected of being linked to Russian interests targeted by the sanctions”, said Captain Veronique Magnin of the French Maritime Prefecture.
A French customs patrol vessel backed by a police surveillance ship and a navy patrol boat diverted the 127 metre (417ft) cargo ship to the port of Boulogne-sur-Mer in northern France in the early hours of Saturday.
Checks were being carried out by customs officials and its crew was “being cooperative”.
Priti Patel also cancelled the visas of the Belarus men’s basketball team, who had been due to travel to the UK for a match in Newcastle. The Home Secretary tweeted: “The UK will not welcome the national sports teams of those countries who are complicit in Putin’s unprovoked and illegal invasion of Ukraine.”