Aarhus Airport/Tirstrup is located 40 km north of Aarhus. There are several daily connections from Copenhagen Airport (flying time 35 minutes) and direct connections to London, Stockholm, and Oslo. The bus from Tirstrup to Aarhus costs DKK 115 one-way (travel time approx. 50 minutes). The final stop is the main train station in the centre of Aarhus. Busses run frequently and are adapted to the the flights. Find the departure that suits you the best right here. If your flight to Denmark goes via Copenhagen, you should try getting a flight directly to Tirstrup/Aarhus airport from there instead of going via Billund.
Billund Airport is located 100 kilometres south of Aarhus and has direct international flight connections to many European cities. The bus ride from Billund to Aarhus takes 1.5 hours, and costs approximately DKK 140 (one-way/cash only). Find the departure that suits you the best right here. Taxi and limousine services are also available.
From Copenhagen Airport, there are direct connections to Aarhus on an hourly basis. The travel time is about 3.5 hours and a one-way standard ticket costs approximately DKK 400 excluding seat reservation (DKK 30).
From Southern and Central Europe, the route goes via Hamburg. Driving from Hamburg takes 4-5 hours by freeway. If you are traveling from other Scandinavian countries, there are ferries to Northern Jutland (Frederikshavn, Hirtshals, or Grenå).