The law was heard and passed on Thursday in the country's federal chamber, the last parliamentary step for a law, by a majority of 37 votes to 20.
The law had already passed the first and larger parliamentary chamber two weeks ago by 98 votes to 67.
The government will now be able to declare a "state of emergency" if the migrant numbers suddenly rise and reject most asylum-seekers directly at the border, including from war-torn countries like Syria.
Interior Minister Wolfgang Sobotka insists Austria - which received 90,000 asylum applications in 2015 and has enforced a cap for 2016 at 37,500 applications - had no other choice as long as "so many other European Union members fail to do their part" to stop the influx.
The Grüne (Green) party are critical of the new rules, however, which they think might be unconstitutional and contradictory of EU law.
Before it was passed in the first level of the Austrian parliament, the head of the Green party Eva Glawischnig said that the law contradicts the European Convention on Human Rights.
“That is an absolute breach of taboo,” she said.
The government wrote into the law that it will abide by international human rights treaties on asylum, although experts say it will be extremely difficult to do this in practice if police are told to turn people away at the border.
“There will be no access for most of the people to the asylum procedure nor for them to check whether there is an infringement on their rights,” Austrian asylum law expert Dr. Christian Schmaus told The Local Austria.
Schmaus added it may be possible that the European Commission, who have the power to investigate national laws, will decide to examine whether Austria's new rules comply with the EU law on asylum.
A spokesperson for the European Commission confirmed to the Local Austria that they have already voiced their concerns with Austria about the law.
"The Commission expects Austria to communicate the new measures swiftly once the legislative procedure has been finalised," said spokesperson Natasha Bertaud.
"This will allow the Commission to fully analyse the political and legal implications of the new measures."
UPDATED: This story was updated at 12:30 to include the comments provided by the European Commission.