"It will no longer happen for migrants who have never worked here a single day or paid anything into the social system to get thousands of euros in welfare!" Heinz-Christian Strache said.
In a post to his 750,000 followers on Facebook, the head of the Freedom Party (FPOe) called it "very important point when it comes to fairness for the Austrian population."
His party late on Friday struck a deal to form a coalition with the conservative People's Party (OeVP) under Sebastian Kurz, who as chancellor will be Europe's youngest leader.
Both parties campaigned for elections in October on platforms of getting tough on illegal immigration and cutting taxes and bureaucracy.
According to their joint programme, monthly payments to asylum seekers will be cut to 365 euros ($430) plus an "integration bonus" of 155 euros. Currently they can get just under 840 euros per month.
The new government was due to be sworn by Austria's president in on Monday at 1000 GMT.
The FPOe has secured the interior, defence and foreign ministries, and the OeVP finance, economy and justice, among others.
The last time the FPOe entered government, in 2000, there was outcry abroad and Austria was ostracised for a time within Europe.
This time, however, with nationalist parties stronger across Europe, including in France and Germany, unease outside Austria has been largely absent.
One exception was European Commissioner Pierre Moscovici, a French left-winger, who tweeted on Sunday that the new Austrian government "requires the vigilance of democrats attached to European values".
"The situation is doubtless different to 2000. But the presence of the far-right is never trivial," said Moscovici, who is EU economic affairs commissioner.
Kurz was due to travel to Brussels on Tuesday to meet European Commission chief Jean-Claude Juncker and EU President Donald Tusk, the foreign ministry said Sunday.
In the past the FPOe has been sharply critical of the European Union.
But Strache and Kurz both stressed on Saturday that their government would be staunchly pro-EU, ruling out a referendum on Austria's EU membership.
However Kurz said that during Austria's presidency of the EU in the second half of 2018, Vienna would press for Brussels to have less say in areas that should be up to member states.
Kurz said that he favours an EU that is "stronger in big questions and which should step back on smaller issues".
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