The insurer, which employs 31,000 worldwide, said moving the centre to Paris made sense given that the French capital is already a major base for Chubb.
It was not immediately clear how many jobs would be moved out of London.
Picking Paris was a "clear choice," said chief executive Evan Greenberg, noting that it already is home to Chubb's Continental European headquarters and a place where the company has extensive history.
Joseph Wayland, executive vice president and general counsel, said the company has received "assistance and cooperation" from the government in Paris "and we look forward to working closely with the French authorities as we move forward on this project."
"We are confident that locating our EU base in Paris will ensure that Chubb is well positioned to serve its clients whatever the ultimate terms of the UK's exit from the European Union."
The Chubb news is a win for French President Emmanuel Macron, who has courted large banks that need to relocate London staff handling EU work when Brexit is finalised.
Some large US banks already have signalled their plans to pick other headquarters cities, such as Dublin (Bank of America) and Frankfurt (Citigroup, Morgan Stanley).
Chubb, which is based in Switzerland but trades on the New York Stock Exchange, has headquartered its EU, and Central and Eastern Europe coverage in London.