A one-day strike will be staged by workers in the Department for Business, Innovation and Skills on Thursday.
The 150 members of the PCS union affected were balloted and the overwhelming majority of the 53 per cent who voted agreed to go on strike.
Earlier this year it emerged the department is planning to close its Sheffield office and move the 247 jobs to the capital.
The union says it is also considering further days of strike action.
PCS general secretary Mark Serwotka said: “This vote sends the clearest possible message to BIS ministers and senior officials that these plans are wrong and must be reversed.
“The closure of this office is precisely the opposite of what the government claims to want for the north and the wider civil service.”
The decision to close the Sheffield office of a major department has contrasted awkwardly with the Government’s commitment to transform the North into an economic “powerhouse”.
Sheffield MPs have mounted a vociferous campaign against the closure and called on the Government to make public the economic case for the decision.
A Commons debate led by Sheffield Central MP Paul Blomfield last week saw MPs pass a motion calling for the National Audit Office to review the move.
The chairmen of two committees of MPs took the unusual step of publicly criticising the senior civil servant at BIS for his failure to properly explain the decision to them.
Former deputy prime minister Nick Clegg has also attacked the move, blaming it on “draconian” cuts to the department.