The centre-left party, led by Prime Minister Anthony Albanese, defeated Scott Morrison's conservative coalition in an election on 21 May.
A record vote for independents and minor parties had made it uncertain whether Mr Albanese would govern in his own right.
But he now has the 76 lower house seats needed, after victories in tight races.
It is a different story in the Senate, where Mr Albanese's government will need crossbench support to pass laws.
About a third of Australians voted for candidates outside the major parties, with support surging for the Greens and independents running on climate platforms.
Mr Albanese has promised a "constructive relationship" with the expanded crossbench, despite not needing to rely on their votes in the House of Representatives. Two seats there remain undecided.
He will announce his cabinet on Tuesday.
The veteran politician, who heads Australia's first Labor government in almost a decade, has promised to adopt more ambitious emissions reduction targets.
However, he has so far refused calls to phase out coal use or to block the opening of new coal mines.
Mr Albanese flew to Tokyo last week for a summit with the leaders of Japan, India and the US, known as the Quad.
His government is also aiming to sure up ties in the Pacific in the face of growing Chinese influence. Foreign Minister Penny Wong made a trip to Fiji within days of being sworn in.
Her visit came as China's Foreign Minister Wang Yi embarked on a tour of small Pacific nations, hoping to secure trade and security deals.
Last month, China and the Solomon Islands agreed a security pact that sparked fears in Australia and the US that Beijing could build a naval base in the region.
