Work on submarine refits is coming to an end
It said the 366 redundancies were inevitable after it lost a contract for further submarine refits to the rival Devonport yard in the south of England eight years ago.
The company announced that the job losses would come amid the "imminent completion" of refit work on the two nuclear Swiftsure class submarines HMS Sceptre and HMS Spartan.
These have been scheduled to leave the Fife yard in December.
Babcock said it would seek voluntary redundancies and would begin a period of consultation with trades unions.
Managing Director, Murray Easton, said: "We naturally regret the impact of this announcement, but the trade unions and our workforce have known that this reduction was inevitable since the decision in 1993 to carry out all future submarine refits at Devonport."
The cuts mean a reduction in the Rosyth workforce to 2,084.
However, Mr Easton remained positive about shipbuilding activity at the yard.
Short-term surplus
He said: "Our core ship refitting business is very healthy and with the recent arrival of the aircraft carrier HMS Invincible, and the welcome news of the award of the third carrier, HMS Illustrious, and the contract to refit five Type 23 Frigates, we clearly have a lot of work ahead.
"Regrettably the major refit of Illustrious will not commence until the end of 2002 and therefore could not prevent the short-term surplus."
The managing director added that the yard had secured non-defence work to "supplement" its main contracts and was seeking further projects.
However, the GMB union said it was shocked at the scale of the redundancies.
"Today's announcement is a legacy from Malcolm Rifkind and the Tory government's 1993 decision to end nuclear refitting in Scotland, favouring Devonport instead," he said.
"What is sad for those losing their jobs today is that Devonport is not even ready to take on the role of nuclear refitting."
Bernie Hamilton, regional officer of engineering union AEEU, plans to seek a meeting with Babcock management as soon as possible.
"The scale of this announcement seems surprisingly excessive and we want to ensure that short-term measures don't undermine the skills base of the dockyard," he said.