Independents Rob Oakeshott and Tony Windsor backed Labor to assist them in forming a minority government on Tuesday.
Their backing gave Labor 76 seats to the coalition's 74 seats after Queensland independent Bob Katter sided with the Coalition.
Ms Gillard travelled to Yarralumla to formally advise Ms Bryce she had the numbers to form a minority government on Tuesday evening.
The prime minister emerged a short time later with a smile on her face but did not speak to the media.
The country's first woman leader, who came to office in a party revolt just 10 weeks ago, scraped over the line to form a government with support from the "kingmakers" after 17 days of frantic post-election negotiations.
"Labor is prepared to govern," a tired-looking Gillard told reporters in Canberra. "I believe the Australian people, given the closeness of this vote, want us to find more common ground in the national interest," she added.
Welsh-born Ms Gillard, 48, narrowly avoided becoming one of Australia's briefest rulers after Tuesday's dramatic denouement, which followed the knife-edge elections on August 21.
Three "kingmakers" split at the last minute, with cowboy hat-wearing maverick Bob Katter siding with conservative opposition leader Tony Abbott -- who came within a whisker of snatching a shock election victory.
Centre-left Ms Gillard's rule was finally confirmed after a lengthy address by Rob Oakeshott, the last independent to declare, who prolonged the prime minister's agony as she watched with Treasurer Wayne Swan.
"I will ... give confidence and supply to government, and in effect that means confidence and supply in Julia Gillard," Oakeshott said.
The Labor leader said she felt a "solemn responsibility" after her rebuke by voters, many of whom turned away from the two main parties last month in Australia's first unclear polls since 1940, when war and the Depression stalked the nation.
"There's no walking away, no attempt to in some way not understand, the message from the result in the election," she said.
"The Australian people have sent me, sent the Labor Party, sent this parliament a message... (I have) heard that message loud and clear."
ms Gillard ended with 76 seats in the 150-seat parliament, with Abbott's Liberal/National coalition on 74, the closest possible margin, capping a rollercoaster period in Australia's usually staid public life.
The MP staged a shock party revolt against elected prime minister Kevin Rudd in June and announced polls just three weeks later, hoping to ride a wave of public support.
But her anticipated honeymoon period failed to materialise as many voters turned to the environment-focused Greens, which enjoyed a record ballot share in a resources-rich country that emerged unscathed from the financial crisis.
The campaign, election and its aftermath have kept Australia's government in limbo for nearly two months, in the worst political crisis since the Queen's representative sacked an elected prime minister in 1975.
Both Mr Oakeshott and Mr Windsor said their main priority was picking the side most likely to provide a stable government capable of seeing out its three-year term and strongly backed Labor plans for a national broadband network.
While Ms Gillard's razor-thin majority leaves her scant room for manoeuvre, Australian National University political scientist John Warhurst said there was little imminent threat of the government collapsing and fresh elections.
"I think they'll be stable, for a good length of time anyway... I think they (the independents) all want to reserve the right to give the new government time to make it work," he said.
"I don't think we'll see instability in the short run."
The kingmakers had given few signals of which way they would fall, leaving Australia's political and media establishment on tenterhooks.
The negotiations moved up a gear in the past 24 hours with Oakeshott meeting Abbott six times on Monday and receiving a package from one of the leaders early on Tuesday -- while he was in the toilet.
The obscure independents, suddenly handed a starring role in the political drama, on Monday announced parliamentary reforms agreed by both sides including having an independent speaker, rather than a member of the ruling party.
