High Court Chief Justice Robert French presided over the ceremonial opening of parliament, which involves the House of Representative members being invited to the upper house.
After the formal opening, members and senators were sworn in, starting with Prime Minister Malcolm Turnbull, Deputy Prime Minister Barnaby Joyce, deputy Liberal leader Julie Bishop and NSW senators.
Earlier, politicians and their families attended a Welcome to Country ceremony in Parliament House's Great Hall.
Tina Brown, dressed in a possum skin cloak and traditional decorations, acknowledged the elders of the Ngunnawal country and welcomed parliamentarians, especially Aboriginal MPs, to Parliament House in Canberra.
"You, along with your fellow and former national leaders, have been meeting here on my ancestral lands for 89 years progressing the social, cultural and economic interests of the nation. I wish you well," she said on Tuesday.
Prime Minister Malcolm Turnbull responded to the welcome by speaking in the Ngunnawal language.
He also noted that next week would make 45 years since Neville Bonner, the first indigenous member of parliament, made his maiden speech.
"Today, as newly elected and re-elected representatives, it is our turn to feel the humility of which Neville Bonner spoke," Mr Turnbull said.
"Our parliament is charged with the responsibility of working with our first Australians as partners and supporters, closing the gap, ensuring that those who were first will no longer be last and as we do, respecting, learning from an enduring culture as old as humanity itself, and as young as these little children who danced for us today."
Opposition Leader Bill Shorten said the Welcome to Country ceremony was a great institution, as was parliament.
He called for the new parliament to rise above "self-seeking, narrow sectional interests" and urged its members to work to make it an even more democratic and representative place.
The parliament welcomed three new indigenous members - Labor senators Patrick Dodson and Malarndirri McCarthy and lower house MP Linda Burney - to join Ken Wyatt and Jacqui Lambie on its benches.
Senators Dodson and McCarthy were ceremonially danced into their new positions in the Senate with a story representing the journey bringing people together from different places and walks of life in finding common ground and goals.
After lunch, Governor-General Sir Peter Cosgrove will deliver a speech outlining the Turnbull government's agenda.
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The coalition enters the new parliament with 76 seats in the lower house to Labor's 69, with five MPs on the crossbench.
It's a different story in the Senate, where the coalition holds 30 seats and will need nine votes to pass laws.
That means negotiating with 26 Labor senators, nine Greens and 11 crossbenchers.
Over coming sitting weeks, controversial first speeches will be delivered by the likes of Pauline Hanson, whose One Nation party won four Senate seats, and former broadcaster Derryn Hinch who won a Senate seat for Victoria.
After three days of sittings the prime minister will jet off to China for the G20 leaders' summit, followed by the East Asia Summit in Laos and the Pacific Islands Forum in Micronesia.
Poll support for Turnbull drops
The Australian's Newspoll of 1696 voters, shows the coalition has lost some support and the party's two party preferred vote was now locked at 50-50 with Labor.
Satisfaction levels with the prime minister have dropped six percentage points since the July 2 election to 34 per cent, which is the lowest level since Mr Turnbull ousted Tony Abbott from office.
Dissatisfaction with Mr Turnbull is up five points to 52 per cent since election day.
Overall, Mr Turnbull is still preferred prime minister compared to Opposition Leader Bill Shorten on 43 per cent to 32.
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The coalition's primary vote has declined from 42.1 per cent to 41 per cent.
Labor's primary vote has risen to 36 per cent from 34.7 per cent on election day.
Deputy Prime Minister Barnaby Joyce played down the poll result.
"You will drive yourself crazy if you start worrying about polls at the start of the political term," he told the Nine Network on Tuesday.
The federal government was busy getting stuck into it and making the hard decisions to take the nation forward, Mr Joyce said.
