After extensive negotiations, the company made a new offer, which members were balloted on and accepted.
Unite general secretary Sharon Graham said: “This is a great result for our check-in members at British Airways.
“By standing together, they have forced a corporate giant like BA to do the right thing and restore levels of pay slashed in the pandemic.”
Unite said the offer, which will be paid in several stages, is worth 13%.
Nadine Houghton, GMB national officer, added: “No one wanted a summer strike at Heathrow, but our members had to fight for what was right.
“This improved pay deal came because of their efforts.
“Now these mainly women workers have won pay improvements for themselves – as well as forcing BA to make this offer to the rest of their staff too.”
A BA spokesman said: “We are delighted with this positive news.”