By Sean Curran
BBC News political correspondent
Tony Blair will hope to leave his troubles at home during this trip to Australia.
Tony Blair looked relaxed during his 2002 Australia trip
He is just in time to catch the last two days of competition at the Commonwealth Games in Melbourne and the Prime Minister and Mrs Blair will be on hand for the closing ceremony.
A tour of the athletes' village is also on the cards.
Mr Blair is making the official visit as a guest of the Australian government.
Announcing the trip, the Prime Minister of Australia, John Howard, said it would provide a "valuable opportunity to discuss the expansion of the Australia-UK relationship, our shared commitment to stabilisation and reconstruction efforts in Iraq and Afghanistan and our common interest in fighting global terrorism".
The political highlight of the trip will come when the British prime minister addresses a joint sitting of the federal parliament in Canberra. This is a rare honour.
Only three world leaders have spoken to the parliament in the past 10 years - US presidents Bill Clinton and George W. Bush, and the President of China, Hu Jintao.
Mr Blair will concentrate on foreign policy with the second of three big speeches setting out his vision of international affairs.
Downing Street says the Canberra speech will focus on the importance of global alliances based on common values.
It follows a speech the prime minister made last Tuesday on the third anniversary of the war in Iraq.
He said there was a worldwide "battle about modernity" and the struggle against Islamic fundamentalism is "not a clash between civilisations. It is a clash about civilisation".
Anti-war protesters have said they plan to hold demonstrations during Mr Blair's visit.
This is the second time Tony Blair has visited Australia as prime minister.
During his last trip in 2002 he was photographed in a T-shirt with a glass of beer in his hand.
Australians have played an influential role in Mr Blair's political life.
Two of his close friends at university were Peter Thomson, an Anglican priest, and Geoff Gallop, who went on to become premier of Western Australia.
Mr Blair's friendship with Australian Prime Minister John Howard, who this year celebrates ten years in power, is of a more recent vintage.
The Liberal leader has been a close political ally over Iraq and Afghanistan. Australia has troops in both countries.
Tony Blair is expected to hold talks with Mr Howard and his Cabinet about security issues and the war on terror.
His other big political meeting with Labor leader Kim Beazley (another old friend) could prove more difficult.
Mr Beazley has called for Australian troops to be pulled out of Iraq and told reporters in Sydney that he would not duck a confrontation over the issue.
Talking about the forthcoming meeting he said "If he (Tony Blair) wants a conversation on Iraq, then I am very happy to say the position I have adopted was that he should have had more patience".
But Mr Beazley also stressed that the two Labour leaders had a lot in common.
He said they shared many views about the future of society and said "many of the views that we developed in government have been picked up subsequently by Tony and implemented in Britain".
Tony Blair will also take part, with John Howard, in the second Australia-UK Leadership Forum in Canberra.
The meeting, to be attended by business leaders and academics, will discuss globalisation, energy security, climate change and skilled migration.