But with six of its major trading partners now in recession, the government fears hundreds of thousands of Australian jobs are now at risk.
"Australia cannot resist the international economic forces and we cannot defy the effects of the downturn in our region," Rudd told parliament.
Under the plan the government will give cash handouts to millions of Australian workers and their families in an effort to stimulate consumer spending.
The first payments are due in March.
The package also includes billions of dollars in spending on roads, schools and housing improvements.
The plan was initially approved by the lower house of parliament, but was rejected by the senate on Thursday.
Unlike in the lower house, Rudd's governing Labor party does not have a majority in the senate.
The stimulus was eventually passed in a second vote on Friday after the government pledged an additional spending package to help revive the country's ailing river system.
That deal secured the support of Nick Xenophon, an independent senator who had voted with the opposition to block the package on Thursday.
Wayne Swan, the Australian finance minister, who led the last minute negotiations with Xenophon to get the stimulus through parliament, said the government was willing to make a deal in the national interest.
"We are prepared to act in the national interest. That's what governs the fiscal stimulus package in the first place," he told Australian radio.
But Malcolm Turbull, the opposition leader, accused Rudd of refusing to negotiate a less costly package of measures.
Turnbull argued the package was too big and would saddle future generations with ongoing government debt.