The upper house Senate voted 39-32 to scrap the charge that was imposed by the former Labor government on major polluters from 2012 in a bid to reduce carbon emissions.
It followed days of protracted negotiations with the minor Palmer United Party, which embarrassed the government last week by pulling its crucial support for repeal of the tax at the last minute.
But powerbroker Clive Palmer won concessions for tougher measures to ensure cuts to electricity and gas prices were passed through to consumers and businesses and the legislation was passed to subdued applause.
"Scrapping the carbon tax is a foundation of the government's economic action strategy," said Abbott, who once claimed evidence blaming mankind for climate change was "absolute crap".
"This is great news for Australian families and for our nation's small businesses.
"We are honouring our commitments to you and building a strong and prosperous economy for a safe and secure Australia," he added.
The government must walk a tightrope in the upper house, needing the backing of minor party senators such as those from Palmer's party to get its legislative agenda passed if it cannot secure support from Labor or the Greens.
Abbott's conservative government says dumping the tax would save households Aus USD 550 a year and strengthen the economy, which is among the world's worst per capita polluters due to its reliance on coal-fired power and mining exports.
Under the carbon tax, the country's biggest polluters paid for the emissions they produced, giving them an incentive to reduce them.
The current administration, the first post-war Australian government not to have a science minister, favours a "direct action" plan that includes financial incentives for polluters to increase their energy efficiency.
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