Aware of the damage that the leadership struggle has caused on the Australian Labor Party, reinstated Prime Minister Kevin Rudd started to mend fences on his first day as leader of the party and the country.

In his first address to Parliament on Thursday, Mr Rudd paid tribute to the woman who ousted him from power three years ago and whom he ousted back on Wednesday night with a 57-45 vote.

The caucus definitely divided the ALP with just a little half, including turncoat Workplace Minister Bill Shorten backing him up, and the remaining members loyal to Ms Gillard quitting their posts.

"Through the difficult years of minority government the former prime minister has achieved major reforms for our nation that will shape our country's future," Mr Rudd said in Parliament.

"On top of all that, I acknowledge her great work as a standard bearer for women in our country; Australia's first deputy prime minister, Australia's first woman as prime minister," he described his former nemesis.

For her part, Ms Gillard congratulated Mr Rudd and shared her thoughts about the recent developments in this video.

Mr Rudd also had kind words for resigned Deputy Prime Minister and Treasurer Wayne Swan.

"No one should forget this work ... I acknowledge the strong work done by the former treasurer assisting me and other members of the cabinet in dealing with the crisis," said Mr Rudd, who was sworn to office on Thursday morning by Governor-General Quentin Bryce as the 28th prime minister of Australia.

To further fix broken ALP ties, Mr Rudd asked MPs to be a little kinder and gentler with each other.

As prime minister again, Mr Rudd is expected to push for moving the election date earlier to August from the original Sept 14 date in the hope of riding high on his resurging popularity to dash Coalition leader Tony Abbott's hope of being Australia's next PM.

Mr Rudd will also announce the cabinet reshuffle on Friday, although he had already introduced Transport Minister Anthony Albanese as the new deputy prime minister and Chris Bowen as treasurer.

Mr Abbott, aware that he lacks the numbers, while criticising the return to power of the potential threat to his political ambition, said he would not file a no-confidence motion.

"The honourable way to become prime minister is at an election ... It's not through some back-door deal with the faceless men, or through some horse-trading with independents on the floor of parliament," The Australian quoted Mr Abbott.

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