The ballot will begin on 21 December and will close on 21 January.
Unite joint general secretary, Tony Woodley said: "Unite is still open to talks but BA must appreciate the strength of feeling across the airline about how badly they've handled this dispute. BA must get serious and work with us to settle the issues."
British Airways said in a statement: "Unite struck a deal in October and reneged on it. The union agreed to hold further talks with us, but has instead issued a strike ballot. Should any industrial action take place, we are confident our contingency plans will allow us to operate normal timetables at Gatwick and London City airports. At Heathrow, we will aim to run a substantial proportion of our short-haul programme and 100% of our long-haul operation."