Previous attempts to gain approval for a new runway have been turned down on environmental grounds.
The airport handled 24 million passengers in 2017 and although it is equipped to accommodate 30mppa, it says that it needs another runway to cope with more long-term demand.
"Flughafen Wien AG welcomes the positive decision of the Federal Administrative Court for the third runway," it says in a statement.
"This represents a forward-looking step towards strengthening Austria as a business and tourism location and giving the aviation location of Vienna an attractive growth prospect.
"The extensive requirements contained in the findings must now be examined on their factual and legal basis.
"We also have to wait and see if the project opponents will appeal to the highest courts against this decision, with a deadline of six weeks.
"This also depends on how the further timetable for the project will be designed; in any case, an implementation decision is only possible if definitive legal certainty exists."