Julia Gillard became Australia’s first woman prime minister Thursday after Kevin Rudd stepped aside as leader of the governing Labor Party, paving the way for the government to drop a controversial new 40% levy on mining profits that has damaged its standing in voter polls.

The Welsh-born 48-year-old former trial lawyer was elected unopposed as leader of the center-left Labor party, a post that carries with it the premiership. Wayne Swan was appointed as her deputy and will retain his Treasury post.

Ms. Gillard’s insurgency was backed by the Labor Party’s right wing but also by key unions on the left.

Her challenge marks an unprecedented fall for the man who ended nearly 12 years of conservative government in Australia. Mr. Rudd swept to power in November 2007, ousting the long-ruling Liberal-National coalition of center-right parties. He saw his popularity slide in recent months after a series of policy missteps.

The party feared that Mr. Rudd, a 52-year-old Chinese-speaking former diplomat, would lead them to defeat in national elections that could come as soon as August.

‘In Australian politics, it is almost unprecedented that a first-term prime minister is dumped by his own party,’ said Roland Randall, a strategist at TD Securities in Singapore.

But Mr. Randall said in a note to investors that ‘for markets, this should not be a destabilizing event’ as Mr. Rudd and Ms. Gillard aren’t far apart on policies.

Driving Mr. Rudd’s reversal have been a decision to shelve a proposed carbon cap-and-trade system meant to fight climate change and a planned tax on ‘super profits’ by Australia’s mining companies-a critical industry for the resource-rich country.

The tax, which the government thought would win popular support by spreading the wealth from the booming mining sector, has instead backfired as the public worries it will damage Australia’s credibility as an investment destination. Mining giants BHP Billiton Ltd. and Rio Tinto Ltd. warned that billions of dollars of investment are at risk, and they have led a fight against the 40% levy, saying it would make Australia one of the highest-taxed jurisdictions in the world.

This criticism has resonated with many Australians who own shares in mining companies, often through pension funds. Mining, a top export sector, helped Australia sidestep the global recession, thanks to demand from developing countries like China and India for the country’s vast stores of iron ore and coal.

Ms. Gillard, elected to Parliament in 1998, has risen swiftly through the Labor ranks and holds the key portfolios of education, employment and workplace relations in the current government.

She has shown sharp political elbows in the past. When a political opponent said in 2007 that the unmarried lawmaker wasn’t qualified to lead the country because she had chosen not to have children, Ms. Gillard shot back that her accuser was ‘a man of the past, with very old-fashioned views.’

Markets initially took the Labor Party mutiny in stride, with the Australian dollar trading higher overseas as the initial shock wore off. Rio Tinto and BHP shares rose in London trading on speculation a leadership change could cause Labor to revisit its controversial mining-profits tax proposal.

Unlike Mr. Rudd, said Mr. Randall, the strategist, Ms. ‘Gillard has not been steadfastly inflexible in her position and would not look weak if she chooses to compromise on the tax.’