Passengers on select BA and American flights to Heathrow from Dallas Fort Worth, New York JFK and Los Angeles will be able to opt into the testing trial, starting 25 November, which will involve three tests throughout their journey.
If they test positive at any stage, they will have to reschedule or cancel their travel.
The first test will be taken 72 hours before departure using an at-home RT-PCR nasal test provided by LetsGetChecked, guided virtually by a medical professional.
If they test negative, they will be able to proceed to their departure airport and fly to Heathrow where they will undergo a second test upon landing, this time a LAMP test administered by Collinson.
Passengers will be provided an at-home saliva testing kit, which they should use to test themselves for a third time three days after arriving into the UK.
BA said the three-test approach "aims to validate a customer’s negative status for Covid-19 throughout the travel journey and provide insight into the most effective and practical testing interval".
"The third test is intended to further confirm the results of the first two tests, to demonstrate that one or two tests will be sufficient to allow travel to safely restart," said BA.
Free tests will initially be offered to eligible customers booked on American Airlines flight AA50 from Dallas Forth Worth, BA flight BA114 from New York JFK and BA flight BA268 from Los Angeles.
The scheme will be expanded to American Airlines flight AA106 from New York JFK at a later date.
A taskforce comprising airline and medical representatives will oversee the trial, and share findings with the US and UK governments and other stakeholders.
BA and American have worked with Heathrow to bring the trial to Terminal 5, with Heathrow now exploring whether trials can be introduced on more UK-US routes.
News of the new trial follows the arrival in the UK on Tuesday (17 November) of the first "Covid-free" flight operated by rival carrier United Airlines, which is trialling a free, optional pre-flight testing programme.
The UK government’s Global Travel Taskforce, meanwhile, was due to present its findings to prime minister Boris Johnson "no later than early-November" after being tasked with exploring ways to reduce the UK’s 14-day quarantine on arrival requirement through testing.
It is understood the taskforce will recommend a "test and release" scheme, allowing those required to quarantine to take a private test at their own expense to release them from quarantine early if they test negative.
Sean Doyle, British Airways chief executive, said: "We know people want to travel but our skies remain all but closed and the UK is being left behind. Major economies like Germany are adopting testing to replace quarantine.
"We need the UK government to introduce a system that allows travellers to take reliable, affordable tests before departure, so they are confident that fellow passengers are Covid-free. For people arriving from countries with high infection rates, a further test on arrival should then release them from quarantine.
"We are confident this approach would open routes, stimulate economies and get people travelling with confidence. The UK’s economic recovery depends on the swift reopening of its skies."
