It is the second time staff have backed industrial action after the first strike vote was overturned by the company on a technicality.
Results released by Unite show that 295 unite members at BBES voted to strike with 145 voting against.
BBES employs 3,063 people with the vast majority non-union members.
HVCA chief executive Blane Judd said: “It’s important to remember that more than 70% of all the workers who have been asked to sign the BESNA agreement have done so.
“There is widespread recognition that the new agreement is the best way to secure jobs, develop skills and compete effectively against foreign firms.”
BBES is one of seven major M&E employers planning to leave the existing JIB pay and conditions deal and replace it with a new arrangement called Besna.
Unite national officer, Bernard McAulay, said: “This high ‘yes’ vote for strike action indicates the resentment felt by our members.”