Julia Gillard has become Australia's first female prime minister after the ruling Labor party installed her as leader.

Disgruntled Labor government members backed Gillard to replace Rudd on Thursday, fearing they would be voted out of office at expected October elections after only one term.

Rudd won a landslide election victory less than three years ago but support for his government has plummeted in opinion polls since April over a series of unpopular policy moves, such as the postponement of a carbon trading scheme.

Rudd was also unable to win support for a controversial mining tax, which had angered miners.

Gillard, Rudd's erstwhile deputy, stood unopposed at a vote of the Labor party's 112 legislators at a meeting on Thursday, hours after a revolt against Rudd.

Rudd's decision not to stand for reappointment was a sign that he knew his support had collapsed.

Since she is leader of the majority party in parliament, Gillard's swearing in as prime minister is a formality.