Under a pilot programme to be launched this week, passengers from selected destinations will be able to upload their coronavirus vaccination certificate before boarding.
On arrival at the airport they will be directed to dedicated lanes at the border to speed their passage through immigration.
The move comes ahead of an expected announcement on Thursday when Transport Secretary Grant Shapps will set out details of the Government's plans to end the requirement for travellers from amber list countries to self-isolate on arrival.
Boris Johnson is said to favour easing the controls from July 19 - when other Covid lockdown restrictions in England are due to be lifted - according to The Times.
Heathrow together with British Airways and Virgin Atlantic - the two airlines involved in the trial programme - said it was essential that there was no delay in implementing the changes.
The scheme will initially involve fully vaccinated volunteers travelling on selected flights from Athens, Los Angeles, Montego Bay, Jamaica, and New York.
Heathrow chief executive John Holland-Kaye said: "This pilot will allow us to show that pre-departure and arrival checks of vaccination status can be carried out safely at check in, so that fully vaccinated passengers can avoid quarantine from July 19."
His comments were echoed by Virgin Atlantic chief executive Shai Weiss who said: "To reap the benefits of the UK's world-leading vaccine roll out, the UK Government must act now to remove self-isolation for fully vaccinated passengers arriving from amber countries, and no later than the domestic reopening on July 19.
"The UK is already falling behind the US and EU and a continued overly cautious approach towards international travel will further impact economic recovery and the 500,000 UK jobs that are at stake."
The call came after Health Secretary Sajid Javid announced people in England who have been double jabbed - as well as the under 18s - will no longer have to self-isolate if they have been in contact with someone who tests positive for Covid-19.
However, there was consternation among some Tory MPs the change will not come into force until August 16, almost a month after other controls are due to have ended.
Mr Javid has acknowledged the numbers of new infections could rise to 100,000-a-day as restrictions come to an end.
Ministers are relying on the vaccination programme to protect people from becoming seriously ill with the virus and prevent the NHS from being overwhelmed.
However former Tory leader Sir Iain Duncan Smith warned the hospitality sector - already ravaged by the economic fallout from the pandemic - could be particularly hard hit by the delay in easing the self-isolation rules.
"Why would you even go to a pub (after step four of the lifting of lockdown)? This makes it worse," he told The Daily Telegraph.
"I wouldn't go to a pub that wasn't still having six around a table and social distancing, otherwise you run the risk of everyone in the pub being pinged and locked down."
Mr Javid said the aim was to "manage the virus in a way that is proportionate to the pandemic" while maintaining as much freedom as possible.