However, the London airport still "strongly encourages" people to continue to wear a face mask, although this will no longer be a firm requirement.
The change came on the same day transport secretary Grant Shapps announced the removal of all remaining Covid-19 travel restrictions and mirrors steps taken by Jet2.com and Tui.
The new rule will apply across all of Heathrow’s terminals, bus and railway stations and office spaces.
British Airways and Virgin Atlantic welcomed the move and signalled they were preparing to follow suit by dropping the face covering requirement onboard their aircraft as soon as regulatory requirements for their destinations allow.
Heathrow said it "will not hesitate" to reinstate the mandatory use of face coverings at the airport should a significant rise in Covid cases or a future variant of concern materialise.
Chief operating officer for Heathrow Emma Gilthorpe said the airport has "worked hard" to keep its passengers and colleagues safe during the pandemic.
"We acted quickly to institute face coverings as one of our first lines of defence, and we’re pleased that we’re now able to move away from a mandatory requirement as society learns to live with Covid longer term," she added.
Meanwhile, Corneel Koster, chief customer and operating officer for Virgin Atlantic, said the airline believes its customers should have the "personal choice" to wear a face mask onboard, on routes where international mask wearing do not apply.
"This policy will be introduced gradually, beginning with our Caribbean services from Heathrow and Manchester airports and we encourage everyone to be respectful of fellow passengers’ mask preferences," Koster added.
Jason Mahoney, British Airways’ chief operating officer, confirmed customers will only be required to wear a face covering onboard flights if the destination they’re travelling to requires it from Wednesday (16 March).
"We welcome this as a really positive step forward," he said. "For destinations where the wearing of a face covering is not mandated, our customers are able to make a personal choice, and we kindly request everyone respects each other’s preferences."
