Of the nearby airports, the most convenient is Istanbul new Airport International in Istanbul, which has flights from all inhabited continents.
There is direct bus service directly from Istanbul new Airport International to Edirne. Departures are at various times with a fare about 11 € and a duration of 2h 30 min depends on trafic jam. You can reach the bus information (it is Turkish but translate via Google to English) from this link.
Istanbul Seyahat Bus service hours starting in underground of Istanbul Airport every day
Of the nearby airports, the most convenient is Istanbul new Airport International in Istanbul, which has flights from all inhabited continents and a bus line providing an easy connection to main bus station (otogar) You can use buses as the cheapest (about 5 euro) (about 40-45 min) to reach bus station (otogar).
The easiest way to reach Edirne is by bus from Istanbul bus station. Departures are at various times with a fare about 12 € and a duration of 2h 40 min depends on trafic jam. The bus station in Edirne is located way out of the city but midibuses will take you to the city center (final stop is near selimiye mosque where city offices of the bus companies are located). Busses (dolmus) also driving to the otogar.
There is two bus companies has service each one hour from 5 am to 11 pm between Istanbul bus station and Edirne.
METRO TURIZM https://www.metroturizm.com.tr/en/
NILUFER TURIZM https://www.nilufer.com.tr/
There are also direct buses to Bulgarian and Greek cities from Istanbul even some other Balkan cities too so they pass over from Edirne too. However, possible to take a taxi to Kapikule, Andreevo (20 km to Edirne city) and Hamzabeyli (40 km to Edirne city) on the Bulgarian border and Pazarkule from Greek border (5 km to Edirne city).
There are two daily trains from Istanbul’s Sirkeci station (one at 8:30 AM in the morning, and the other at 3:50PM in the afternoon. Both arrives in Edirne about four hours later). Trains from Europe to Istanbul also call at the station. There are also European train too.
The main station (signed as Edirne Gar on the station building) lies about 4 km east of downtown, close to the main avenue heading eastern suburbs of the city (which is also the main highway to Istanbul). However, all trains to Edirne drive onward west to Kapıkule (main borderpost on Bulgarian border) and call at Edirne Şehir station on the way, too, which is little more than a platform next to the rail tracks, lying less than a kilometre away from downtown to southwest, on the edge of the old quarter (Kaleiçi) and close to the banks of Tunca.
The city is on the main highways linking Turkey and Europe (road numbers: toll-free D100 and toll-road/motorway O-3/E80). A drive takes no more than two hours from Istanbul (224 km away) to Edirne on the motorway, even less if you drive very fast. The main European-Turkish border post Kapikule/Kapitan Andreevo (between Turkey and Bulgaria, SE of Svilengrad) is about 15-20 km away from the city, while less significant Pazarkule border post (between Turkey and Greece, north of Orestiada) is even nearer.