The new law aims to promote what conservative Integration Minister Sebastian Kurz calls an "Islam of European character" by muting the influence of foreign Muslim nations and organisations, and offering Austrian Muslims a mix of increased rights and obligations in practising their faith in the central European country.
Austria's previous "law on Islam" dates from 1912, after the annexation of Bosnia-Herzegovina by the Austro-Hungarian empire.
The two-year-old bill passed by parliament today predates the recent jihadist violence in France and Denmark, but is designed to "clearly combat" the growing influence of radical Islam, Kurz said.
Earlier this month French Prime Minister Manuel Valls similarly raised the notion of banning foreign funding of Islamic organisations. Kurz says officials in Germany and Switzerland have also expressed interest in the legislation.
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Passage of the law comes amid estimates indicating around 200 people from Austria including women and minors have gone to Syria and Iraq to join jihadist militias like Islamic Front.
A poll published by the OGM institute yesterday found 58 per cent of Austrians feeling radicalisation of the nation's Muslims was underway.
It also requires the nearly 450 Muslim organisations in the country to demonstrate a "positive approach towards society and the state" in order to continue receiving official licensing.
Imams will be obliged to be able to speak German under the law, a bid to make their comments more accessible and transparent, while also facilitating the fuller integration of Islam into wider Austrian society.
"We want a future in which increasing numbers of imams have grown up in Austria speaking German, and can in that way serve as positive examples for young Muslims," Kurz explained ahead of the vote.