GMB and Unite members - who are mostly check-in and ground workers - had planned to take industrial action over the summer, after a 10% pay cut imposed on them by BA during the pandemic was not reinstated.
However this has now been suspended after the unions accepted a deal with a pay rise, a one-off bonus and the reinstatement of shift pay.
The offer, which will be paid in several stages, is worth 13% for the British Airways workers.
Nadine Houghton, GMB national officer, said: “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.
“Our members stood up for themselves and fought for what they were owed.
“These are frontline workers facing harassment and abuse from customers daily.
"The least they deserved is fair pay.”
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.
“This is a further example of how Unite’s relentless focus on winning better jobs, pay and conditions for its members is delivering.”
Unite regional officer Russ Ball added: “Special praise needs to be given to Unite’s reps, who were critical to ensuring this dispute was a success.
“Their hard work, dedication and commitment has been essential to ensuring that members had the confidence to support industrial action and that workers were fully informed throughout the dispute.”
However that was suspended after a “sustainably improved offer was made” following negotiations with conciliation service Acas.
Today, members accepted a 12.5% pay rise, along with an increase in weekend overtime rates as well as a £2,500 bonus.
This strike action would have affected 70 airlines at the airport including Virgin Atlantic, American Airlines, United, SAS, Air France, Emirates, Delta, JAL, KLM and Singapore Airlines.