It was the second month in a row passenger numbers breached the million barrier, making it a record summer for the airport.
To celebrate, the company bought a cup of coffee for each passenger who flew out of the airport yesterday. Chief executive Gordon Dewar said: "What a truly remarkable summer we have had.
"We want to thank each and every one of the two million passengers that travelled with us in July and August for choosing our airport and helping us to break records.
"It is amazing to think that we have had enough people pass through our terminal to fill almost 4000 Airbus A380s."