Passenger numbers at rivals Glasgow increased even faster in what was its best July for seven years.
Aviation experts said the figures reflected the strengthening economy as people flew more and airlines increased flights.
However, they questioned how long it would continue.
Edinburgh’s total was up by 10.3 per cent to 1.2 million on a year ago, with underdog Glasgow climbing even faster, by 13.7 per cent to 956,000.
Aberdeen airport fared less well, with UK passengers down 5.9 per cent but international fliers up by 1.8 per cent. Helicopter traffic was down 14.8 per cent.
Edinburgh, which has struggled with chronic security queues, said last month’s figure was “a phenomenal achievement but it hasn’t come easily”.
Among the latest passengers to complain was Derek Ross, who tweeted yesterday: “Edinburgh Airport new security Hall. Shambles. #edinburgh #chaos.”
Airport chief executive Gordon Dewar said: “Our teams have worked hard to help passengers on their journey and we’re continuing to work hard to give our passengers the service they expect.
“It was only two years ago, we broke our first million passenger month and now in our peak we’ve grown by 20 per cent. “This is really pleasing, but it’s clear we’re going to have to invest further for next year as we anticipate more growth.”
The extra passengers included golf fans heading for the Open at St Andrews, Ryanair’s restored Stansted services and more frequent British Airways and Flybe flights to London City.
Glasgow’s increase was its seventh month in a row of growth of more than 10 per cent.
Contributing to the increase was WestJet’s new route to Halifax in Nova Scotia and Wizz Air’s new Budapest service. There was also “strong demand” for Ryanair’s and BA’s London flights.
Last week, airport trade body ACI Europe named Glasgow as one of the continent’s fastest growing airports for the first half of this year.
Managing director Amanda McMillan said Glasgow had seen “exceptional growth” in 2015.
She said: “July has been rewarding from a route development perspective, with EasyJet’s new service to Milan, and Balkan Holidays unveiling a new service to Varna in Bulgaria.”
“August is set to be another record month as we welcome visitors from across the globe for major events such as the World Pipe Band Championships and the UDO Worlds X Street Dance Championships – both of which will take place in the city.”
Passengers numbers have grown at Edinburgh by 6.6 per cent over the last year to nearly 10.7 million, with Glasgow putting on 10.5 per cent to 8.3 million.
Gerald Khoo, transport analyst at brokers Liberum, said: “These are impressive growth rates from both airports, the result of competition between the airlines and the airports.
“Growth might slow next year against these tough comparatives, especially if intense competition leads to some attrition of services.
“However, this might be offset by further improvements in long-haul services.”
Aviation analyst Laurie Price said: “Inevitably, the underlying growth will be attributable to the strength of the economy and scale of the recovery.
“Lower fuel prices will also have helped the airlines.
“The key will be to see that the level of growth can be sustained year-round, not just in peak summer.”
Mr Price said more long-haul routes might be established if WestJet’s new route, using a Boeing 737 – the size of plane operated by Ryanair on European flights – was successful.
He said: “Innovative services by WestJet, with novel use of hitherto short-haul aircraft on long-haul operations, may pave the way for similar year-round operations from Scotland in the future, increasing both the network and frequency available.”