Edinburgh Airport said more than 781,000 passengers passed through its doors last month, a year-on-year increase of 11.7%.
Glasgow saw its traffic rise by 8.4% to nearly 600,000.
Meanwhile, Aberdeen International Airport reported its lowest decline in passenger numbers for almost two years.
Edinburgh said most of its growth last month came from international flights, which were up by 11.6% on the same period last year.
Airport chief executive Gordon Dewar: "After a record-breaking 2016, it is fantastic that we start 2017 with strong figures.
"We are now seeing the impact of launching 27 international services in 2016. "
At Glasgow Airport, international passenger numbers grew by 16.1% as a result of strong demand on routes to Toronto, New York and Dubai.
EU-scheduled traffic was up 21.4%, following a rise in capacity on some winter sun services and city breaks.
Domestic traffic grew year-on-year by 2%, with increased uptake reported on routes provided by British Airways, Easyjet and Flybe.
Glasgow Airport managing director Amanda McMillan said: "Last year was our busiest on record, so it's pleasing to see this momentum has continued into 2017 with our best-ever January passenger numbers."
Meanwhile, Aberdeen International Airport recorded its lowest decline in passenger numbers for almost two years in January.
A total of 207,100 passengers travelled through the airport during the month, 1.7% fewer than a year ago.
Domestic traffic rose by 0.6%, while international traffic fell by 2.5%.
Helicopter traffic was down 7%, which the airport attributed to "inclement weather conditions in overseas locations" and the temporary recall of Sikorsky S92 helicopters early in the month.
Airport managing director Carol Benzie said: "It's hugely encouraging that last month we saw our lowest decline in passenger numbers since March 2015, which is a fantastic start to the year.
"I'm delighted that our domestic traffic increased and I'm confident that the overall figures would have been even healthier had our helicopter traffic not been impacted by a maintenance recall."
Ryanair is to extend its Aberdeen schedule in May by introducing a new link to Faro, which will coincide with the relaunch of Air Baltic's Riga route, as well as new flights to the Faroe Islands with Loganair.
Scotland's two busiest airports have recorded their best January on record, following a marked increase in demand for international travel.