Members of the GMB and Unite unions had voted for industrial action in a row over a pay cut during the pandemic.
After extensive negotiations, the company made a new offer, which members were balloted on and accepted.
Earlier this month, British Airways' check-in staff at Heathrow suspended a strike after the airline agreed to improve its pay offer.
This week, fuel workers at Heathrow Airport also called off a strike which would have coincided with the start of the UK's school summer holidays.
The beleaguered airport is already suffering from delays and caps on passenger numbers owing to staff shortages. The chairman of Heathrow, Lord Paul Deighton, has laid the blame for travel chaos on airlines failing to recruit enough baggage handlers.
Staff represented by the GMB and Unite unions voted to approve their respective pay offers from British Airways, they said on Friday.
“No one wanted a summer strike at Heathrow, but our members had to fight for what was right,” said Nadine Houghton, national officer for the GMB union.
GMB said workers would now receive a consolidated pay rise of 8 per cent, a one-off bonus and the reinstatement of shift pay.
In addition, more than 500 members of Unite, who initially voted in favour of industrial action over a pay dispute with British Airways, also accepted a new pay offer.
Unite said the offer was worth a 13 per cent pay rise for staff, which will be paid in several stages.
Any strike at Heathrow could have further pressured an aviation industry struggling with staff shortages, which have resulted in long queues and cancelled flights amid increased demand from travellers after the Covid-19 pandemic.
Representatives for British Airways did not immediately respond to a request for comment.