The decision by the two independent MPs gives Labor a parliamentary majority of 76 seats to the Coalition's 74, continuing Julia Gillard's prime ministership.
The pair gave a joint press conference, but announced their decisions separately, adding to the suspense of two and a half weeks of national political limbo.
Mr Windsor cited the National Broadband Network as a primary reason for his backing.
"You do it once you do it right and you do it with fibre," he said, adding that climate change policy was also an important factor in his support.
Mr Oakeshott, in a lengthy justification for his support, said it was "not a mandate for any one government, nor was it an endorsement".
The historic decision comes after intense wall-to-wall negotiations between the country independents and Ms Gillard, Opposition Leader Tony Abbott, ministers, ''shadows'' and officials.
It brings a welcome end to the impasse which has meant the continuation of a ''caretaker'' situation well beyond the election - and a lack of capacity for substantive decisions to be made.
This is Australia's first hung parliament since the 1940s.
Earlier this afternoon, the impasse took an extraordinary turn with Queensland independent Bob Katter calling a press conference to announce his decision ahead of fellow independents Mr Oakeshott and Mr Windsor.
While he announced he would support the Coalition in a minority government, the Queensland independent also indicated he could switch sides in the interests of stability.
"I would put it to you this way: I would most certainly see a moral responsibility to look at the issue of stability," he said.
Despite promises that today's result will bring stability, the House of Representatives will be difficult to manage, with the fate of legislation an item-by-item proposition.
The independents insist the arrangement will give scope for more flexibility and consensus than we have previously seen.
But critics fear it will be difficult for the government to be able to do much at all, let alone take hard decisions and drive reform.
While the three country independents made the final decision on who would form government, a total of six cross-bench MPs will determine the fate of bills in the House.
The others are the Greens' Adam Bandt, Tasmanian independent Andrew Wilkie and WA National Tony Crook.
The deals the various independents have done only relate to matters of supply and confidence motions - they do not bind these MPs on ordinary legislation.
The fortnight of haggling has brought a plan for dramatic change in how the House of Representatives works, including a tighter, more stream-lined question time, a more independent speaker and the prospect of conscience votes on private members bills on controversial subjects including gay marriage.
The country independents put more effort into winning changes in process - including how the Parliament works and putting regional Australia closer to the centre of decision-making - than into obtaining ''pork'' for their own electorates.
But they can be confident that ''pork'' will flow over the time ahead, not least because the uncertainty on legislation means the wooing can't stop now.
Both Ms Gillard and Mr Abbott have devoted their full attention, and many hours, to listening to and trying to accommodate the country trio over the past fortnight.
With the skill of poker players, the country independents kept both sides guessing right up until yesterday.
They were tough, polite but enigmatic in their public utterances and private discussions, a strategy designed to extract most from either side.
Their initial decision to act as a group, despite their diversity, strengthened their hands.
They have won praise from both sides. But their decision will now sharply separate their friends and their foes.
Michelle Grattan is the political editor for The Age.
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