According to the British Airline Pilots Association (BALPA), 94% of the pilots who voted agreed to the pay cut, which will save the airline £26 million per year.
Jim McAuslan, BALPA general secretary, said: "This is an unaccustomed position for a union to be in but we have pressure tested the company's trading position and cost base and are satisfied that this step is necessary to help British Airways recover its position as one of the world's most successful airlines.
"Our members have backed that judgment and are leading the way in contributing to the turn-round plan. The package of measures will be implemented as soon as British Airways demonstrates delivery of the cost-saving targets across the whole company."
The company has also been in negotiations with trade unions and ACAS for several weeks over a proposed two-year pay freeze and 3,700 job losses.
This morning, a spokeswoman from British Airways told HR magazine: "We are pleased that BA pilots have voted overwhelmingly in favour of the cost-saving package. It involves a combination of reduced pay and increased productivity.
"Our engineers have also already voted in favour of changes to their working practices.
"Talks with our remaining trade unions, facilitated by the conciliation service ACAS, are taking place. In line with our previous practice, we will not be making any public comment on the content of these discussions."
British Airways pilots to take pay cut as part of airline's cost-saving package
British Airways pilots have agreed a 2.6% pay cut.
