Omega Underwriting Holdings has become the second insurer within a week to abandon London and re-domicile in Bermuda.
The insurer has been given authorisation by the Treasury and Revenue & Customs to set up a new holding company in Bermuda on9 November.
Last week, Hiscox announced it would move its domicile to Bermuda by the end of the year to take advantage of the tax regime.
Richard Tolliday, chief executive of Omega, said the move to Bermuda made "absolute strategic sense".
He said: "Most of the group's profit comes from US insureds and reinsureds, and the strategic focus of the group has always been weighted towards the US.
"There is no question, however, of this affecting our support for all the operating platforms within the group."
Andrew Green, tax partner at financial adviser Mazars, said the big question now was which company would be next to re-domicile.
"It could be any of [the Lloyd's insurers]," he said.
"I expect they will all be looking at it. In fact, I am sure they all are."
Meanwhile Omega has set up a US subsidiary to write surplus lines business.
This follows Omega's announcement of pre-tax profits of £4.8m for the first six months of 2006, a 10% increase on the same period last year.