However, the rebound has been slower for UK flights and within the common travel area, including Ireland and the Channel Isles, with traffic only 65 per cent of pre-Covid levels in June.
Scotland’s busiest airport said its July figures were similar but predicted overall passenger figures would not return to 2019 levels until the end of next year.
The dramatic increase has triggered major problems for airlines’ baggage handling firms because of staff shortages, with thousands of bags piling up at the airport.
The latest official figures show Edinburgh’s passenger total increased to nearly 1.2 million in June – 84 per cent of the 1.4m passengers in June 2019.
The figures compare to just 176,000 a year ago and 19,000 in the same month in 2020.
Edinburgh Airport said its passenger total so far this year was 70 per cent of pre-pandemic levels, which is expected to increase to 75 per cent by the end of the year.
But international traffic has reached 95 per cent of 2019 levels.
The airport’s 6-7am morning peak was at 90 per cent of pre-pandemic levels in June, with a higher proportion of leisure flights than traditionally business-traveller dominated services, such as to London.
An airport spokesperson said: "It's encouraging to see the recovery trend continuing and it demonstrates the pent-up demand for travel we knew was always there.
"The fact our transatlantic travel is fully recovered is hugely positive.
"Aviation has different partners involved in many moving parts, and we need all of these parts to be working perfectly and in sync to provide the best possible experience for passengers.
"Clearly there have been some issues, as we warned there would be, but thankfully our operation has performed relatively smoothly and we've seen improvements in security, resulting in quicker clearance times and shorter waits.
"We know partners such as baggage handlers continue to face some issues across their network and we continue to support them when and where we can."
United Airlines, whose flights between Edinburgh and New York, Washington DC and Chicago resumed from March after a two-year suspension, said: “Across all of our services from Scotland, we are seeing booking levels in line with pre-Covid levels and an unprecedented demand for leisure travel, which has exceeded our original expectations.
"We’re also seeing business travel rebounding more quickly than expected.”
Glasgow Airport said it expected 70 per cent of pre-Covid passengers this year and full recovery not until 2025, but UK traffic had been up to 85 per cent of 2019’s.
Anna Hughes, director of behaviour change charity Flight Free UK, said: It’s undeniable that there is a pent up demand for travel, but as the climate crisis grows ever closer it’s disingenuous to celebrate more planes in the air.
"What we need instead is a carefully managed programme of de-growth and a move to alternative forms of transport so we can still access the benefits of travel without the huge impact upon the climate.”
Scottish Conservatives transport spokesperson Graham Simpson said: “Our thriving tourism sector is one of Scotland’s greatest assets and it’s wonderful to see Edinburgh Airport attracting so many passengers.”