Travel by land
There is a bus service between Tartu and neighbouring countries in the south and east. The service is provided by Lux Express, Eurolines, and Ecolines.
Some buses between Tallinn–Tartu also have a scheduled stop at the airport. However, not all buses have on-demand stops at the airport, meaning that you should make sure to choose the correct line. Information on bus lines and stops can be found HERE. The airport bus station has a self-service ticket dispenser where you can buy tickets for buses stopping at the airport on the way to Tartu. The machine accepts card payments.
Tartu is also accessible by train from Tallinn (service provided by Elron) and the stop to board the train is Ülemiste. In order to get to the stop you have to leave the airport in the direction of Ülemiste shopping centre and pass through the shopping centre.