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.
