Edinburgh Airport said nearly 1,142,000 people passed through its doors last month, an increase of 13% on the figure for last year.
Glasgow recorded an 8.9% increase on April 2016, with more than 786,000 passengers.
Both airports attributed their strong performances to a sharp rise in international passenger numbers.
Aberdeen International Airport also reported an increase in its figures.
Edinburgh said international traffic was up 20.4%, following the launch of 27 new international services over the last year.
Edinburgh Airport chief executive Gordon Dewar said: "Our expansion of routes and destinations is good news for travellers and it also creates new jobs, opportunities and offers greater international links for people in this city and for all of Scotland."
An 18% increase in international traffic helped Glasgow Airport record its 50th consecutive month of growth.
The airport attributed the rise in part to strong demand for its growing list of European destinations, including Ryanair's new services to Valencia, Lisbon and the Lithuanian city of Palanga.
Airport managing director Amanda McMillan said: "In addition to growing our European network we have been working hard to consolidate our long-haul offering.
"Both American Airlines and WestJet will return later this month and we also welcome Delta Air Lines to Glasgow for the first time when its inaugural service to New York-JFK takes off on 26 May."
Meanwhile, Aberdeen International Airport's recent improvement in passenger numbers continued last month.
It reported an increase in both domestic and international traffic, after almost 252,000 people travelled through its doors.
Domestic and international traffic were up 2% and 0.5% respectively, which the airport said was due in part to the introduction of a number of new routes, namely Ryanair's direct flights to Malaga and Alicante and Flybe's new Heathrow service.
However, helicopter traffic was down 17.4%.
Airport managing director Carol Benzie said: "It is extremely encouraging to see our international and domestic traffic perform well.
"We have added nine new routes over the course of the past year and this has contributed to us seeing a slow but steady increase in fixed-wing passengers."
Scotland's two busiest airports have reported record passenger numbers for the month of April.