A total of 770,265 people passed through the capital's airport last month, making it the busiest February ever following a rise of 17.2% on the previous year's figure.
Glasgow Airport saw a 14.1% increase, which took the number to 582,879 passengers for the month.
It follows positive figures for the airports for January as both reported annual increases in passenger numbers compared to 2015.
Gordon Dewar, chief executive at Edinburgh Airport, said: "February's passenger numbers have broken another monthly record and act as further indication of just how big Edinburgh Airport's global ambitions are.
"We have seen a massive increase of 30.4% in the number of international passengers and this highlights the growing draw of Edinburgh as a prime global destination."
At Glasgow, international traffic grew by 13.2%, which bosses said was due to strong demand on European routes to Berlin, Reykjavik and Milan.
Domestic services increased by 14.8%, with Flybe's routes to Exeter and Cardiff proving popular, while British Airways, easyJet and Ryanair also reported strong demand for their London flights.
Airport managing director Amanda McMillan said: "This year marks a huge milestone for the airport as we celebrate our golden anniversary year.
"What makes that even more exciting is the fact that we are continuing to see our passenger numbers grow at record rates, following our success in 2015 securing more than 30 new routes and services."