The new coalition was agreed on Friday by the conservative People's Party (ÖVP) and the Freedom Party (FPÖ), pledging to stop illegal immigration, cut taxes and resist EU centralisation.
It will be led by Chancellor Sebastian Kurz, who took over the ÖVP in May and yanked it to the right, securing his party first place in October elections. At 31, Kurz will be the world's youngest leader.
At his side for the investiture by Austria's president in the Hapsburg dynasty's imperial palace in Vienna was FPÖ chief Heinz-Christian Strache, 48, now vice-chancellor, and FPÖ general secretary Herbert Kickl, the new interior minister.
Strache has said Islam "has no place in Europe" and last year called German Chancellor Angela Merkel "the most dangerous woman in Europe" for her open-door refugee policy.
On Sunday, Strache trumpeted to his 750,000 followers on Facebook that the new government would slash social benefits for asylum-seekers.
"It will no longer happen that migrants who have never worked here a single day or paid anything into the social system will get thousands of euros in welfare!" he said in a post that has gained 9,000 "likes".
Kickl is a former speechwriter for Strache's predecessor Jörg Haider, whose 2000 entry into government prompted an outcry and soul-searching in Europe that appear largely absent this time.
More than 2,000 people took part in demonstrations on Monday, AFP reporters said, brandishing placards such as "refugees welcome" and "Nazis out" and "No Nazi pigs".
A heavy police presence of about 1,500 officers, with helicopters overhead and water-cannon trucks at the ready, blocked off the area around the Hofburg palace.
At one point police fired a smoke grenade when some protestors tried to break through a barricade, an AFP photographer said.
In 2000, several hundred thousand people took to the streets.
The FPÖ also obtained the defence and foreign ministries, while the ÖVP got finance, economy and justice amongst other portfolios, and will continue to handle EU affairs.
Both Kurz and Strache won over voters two months ago by stoking concerns about immigration after the record influx in 2015, mirroring elections elsewhere in Europe this year.
Geert Wilders' Freedom Party became the second-largest in The Netherlands, Marine Le Pen of France's National Front was in a runoff for the presidency and the Alternative for Germany entered the Bundestag.
But the FPÖ is rare in western Europe in having translated success at the ballot box into real power.
Speaking at a far-right congress in Prague on Saturday, Wilders said the FPÖ's entry into government was "an excellent result", while Le Pen called it "very good news for Europe".
"Every election demonstrates a form of rejection of the European Union," Le Pen said, echoing the euro-scepticism shown by the FPÖ in the past.
Both Kurz and Strache emphasised however on Saturday that Vienna would stay staunchly pro-EU and that their plans for more Swiss-style "direct democracy" excluded a referendum on EU membership.
But Kurz said that during Austria's presidency of the EU, set for the second half of 2018, Vienna would press for Brussels to have less say in areas that he believes should be up to member states.
Kurz said he envisions an EU which should be "stronger in big questions and which should step back on smaller issues".
Kurz also said that Austria would not change its line on supporting EU sanctions on Russia imposed over Ukraine, even though the FPÖ, like other far-right groups, wants them lifted.
But according to their joint programme, Austria will "actively work" towards easing the sanctions "in unison" with the rest of the EU.
In addition the new government's programme says that Austria will seek support to "definitively" end Turkey's bid to join the EU, sparking anger on Sunday from Ankara.