After a day of speculation, BNFL issued a statement saying that John Taylor was leaving after four years in the job.
BNFL chairman Hugh Collum said: "We now have the opportunity to move ahead with a fresh sheet."
There was also speculation that other senior managers could leave over the scandal.
A BNFL spokesman said: "The review of management has not been completed."
We now have the opportunity to move ahead with a fresh sheet
BNFL chairman Hugh Collum
A damning report published last week by the Nuclear Installations Inspectorate confirmed that some safety records had been faked at the company's plant at Sellafield in Cumbria.
Mr Taylor initially refused to step down, despite further findings in the report of "systematic management failures".
But the pressure on him mounted, and Trade and Industry Secretary Stephen Byers had issued a statement welcoming his decision to step down, even before it was officially confirmed by the company.
Mr Byers said: "In the circumstances, it was the appropriate course of action.
"We can now look forward to a fresh start at BNFL under a new chief executive."
But union leader Jack Dromey, of the Transport and General Workers' Union, said the departure of Mr Taylor was "rough justice" for a good chief executive.
"It is sadly clear that the company's customers are demanding change at the top if confidence is to be restored. He is the victim of past failures rather than
personal failures," said Mr Dromey.
He is the victim of past failures rather than personal failures
Union leader Jack Dromey
A replacement could be announced as early as this week.
The upheaval at the company could force the government to postpone plans to
part-privatise BNFL before the next election, amid concern about the
long-term survival of the Sellafield plant.
But Mr Collum said on Monday he was confident that the planned partial privatisation of BNFL could be achieved, "although perhaps delayed."
Threatened
The data which was falsified related to checks on the safety of a shipment of uranium and plutonium mixed oxide fuel (Mox) to Japan.
Kansai Electric Power, the firm's biggest Mox fuel customer, has threatened to
withdraw its custom and has demanded that the consignment sent to Japan last
December be returned to Britain.
The nuclear inspectorate has set BNFL a deadline of mid-April to tighten safety or face closure
of the Sellafield plant.
Mr Taylor's resignation won no praise from environmental campaign group Friends of the Earth.
"Re-arranging deck chairs on a sinking ship is no help to anyone. BNFL only has
a long term commercial future if it changes the very nature of what it does," said Dr Patrick Green, senior nuclear campaigner for Friends of the Earth.
BNFL would not confirm reports that Mr Taylor will receive a leaving package of £300,000.
