Ms Gillard, who was deputy prime minister, has vowed to end division over a controversial mining tax, resurrect a carbon trade scheme and call elections within months.
Mr Rudd made an emotional and ignominious exit, quitting just before the Australian Labor Party was to dump him in a ballot and less than three years after a stunning election victory in 2007.
The Rudd government's dramatic slide in support this year sparked fears within the ruling party of an electoral defeat at a poll expected around October.
'I asked my colleagues to make a leadership change because I believed that a good government was losing its way,' Ms Gillard told a news conference.
Ms Gillard, 48, immediately offered to end a bitter dispute over a controversial 'super profits' mining tax, which is threatening €16bn worth of investment and has unnerved voters.
But Ms Gillard stood firm on the introduction of a resource tax, stressing that miners should pay more tax and adding in parliament later that miners had conceded they could pay more.
'To reach a consensus, we need to do more than consult, we need to negotiate,' she said, adding the government would end its mine tax advertisements.
Mr Rudd became the shortest-serving Australian prime minister since 1972, with his leadership falling apart after a string of poor opinion polls.
He said: 'I have given my absolute all. I was elected by the Australian people as the prime minister ... to bring back a fair go for all Australians.'
