IT changes will cost an estimated £280,000 and moving staff and materials £20,000, an FOI request revealed.
The business secretary was stripped of his role overseeing media competition issues after being recorded saying he had "declared war" on Rupert Murdoch.
Culture Secretary Jeremy Hunt is taking on those responsibilities.
Two full-time members of staff have been organising the move between the Department for Business, Innovation and Skills to the Department for Culture, Media and Sport.
The figures were given to the BBC following a Freedom of Information request. The government said the estimated total cost was £300,000.
A government spokesman said: "Responsibility for all competition and policy issues relating to media, broadcasting, digital and telecoms sectors has been transferred from the Secretary of State for Business, Innovation and Skills to the Secretary of State for Culture, Olympics, Media and Sport.
"The transfer of staff and associated resources is being handled as cost effectively as possible."
Mr Cable was secretly recorded by undercover Daily Telegraph reporters in December saying: "I have declared war on Mr Murdoch and I think we are going to win."
The Telegraph published some comments made by Mr Cable, but not those about Mr Murdoch - which were then leaked to the BBC's business editor Robert Peston.
Culture Secretary Mr Hunt has given News Corp more time to make alterations to their bid for full control of BSkyB after the media watchdog Ofcom recommended it be referred to the Competition Commission.
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Ok, aside from fact that Vince was an idiot (btw Vince thanks for increasing CGT to 28% you ****
) how the fook it can possibly cost £280k in IT stuff with other costs being £20k??!
