The coalition between the conservative People's Party (ÖVP) and the far-right FPÖ has pledged to stop illegal immigration, cut taxes and resist EU centralisation.
It will be led by Chancellor Sebastian Kurz of the ÖVP, who at 31 years old is the world's youngest leader.
His deputy is FPÖ leader Heinz-Christian Strache, 48, who last year called German Chancellor Angela Merkel “the most dangerous woman in Europe” for her open-door refugee policy and has warned about the “Islamisation” of Europe.
After meeting with Kurz in Brussels, Juncker said he did not want to comment on the new government, saying “I am against any bias.”
“This government has taken a position that is clearly in favour of Europe and that is what counts for me,” he added.
“We will judge this Austrian government, as we do all governments, on its actions” he said, adding “what was in the government's programme suits us almost 100 percent.”
Kurz, who has increased his pro-EU statements despite an alliance with the eurosceptic and pro-Russia far-right, continued in the same vein in his comments on Tuesday.
He said he wanted to “strengthen Europe” on “important issues” but he expressed his desire that its role be reduced in smaller matters.
“We are a pro-EU nation, we are a pro-EU government,” he added.
EU President Donald Tusk, who also met Kurz, also withheld criticism of the new government.
“I see in (Kurz) an energetic, determined and pro-EU leader,” Tusk wrote on Twitter.
The last time the FPÖ entered government, in 2000 under Jörg Haider, there was outrage across Europe that a man who praised Adolf Hitler's “orderly” employment policies could be part of an EU government.
But this time, with Europe more inured to far-right parties and the FPÖ appearing to have mellowed, the reaction has been muted.