Mr Blair's North American visit begins on Wednesday night when he arrives in the Canadian capital, Ottawa.
Mr Blair, who was close to Mr Bush's predecessor Bill Clinton, has had two telephone conversations with the new "leader of the free world" since he became president.
Defence and trade issues are likely to be high on the political agenda when the two meet for the first time at the presidential retreat at Camp David, Maryland on Thursday.
The meeting of the two leaders comes less than a week after Britain and the US jointly launched air strikes on Iraq for breaching the southern no-fly zone.
Mr Blair's North American visit begins on Wednesday night when he arrives in the Canadian capital, Ottawa.
He will be meeting Canadian Prime Minister, Jean Chretien, who himself met Mr Bush earlier this month.
Mr Chretien, who was re-elected in November, may be able to offer Mr Blair some tips, with a General Election in the UK widely expected this spring.
Accompanied by his wife, Cherie, Mr Blair will head for Washington on Thursday, where he will meet with Vice President Dick Cheney before flying to Camp David for talks.
Reviewing sanctions
Last week's air strikes in Iraq have
driven a wedge between Europe and the Anglo-American alliance.
The action has strained Mr Blair's ties with European partners, who are carving out an independent military role within NATO.
Britain stands by the bombing, but the government said on Tuesday it was joining with the US to review sanctions imposed on Iraq, in order to alleviate the impact on ordinary people.
Some European countries also fear President Bush's plans for a ballistic missile defence shield - dubbed 'Son of Star Wars' - may trigger a new arms race.
The UK Government has been cautious about the plan, but says it understands American concerns.
"It is a very sensitive issue," Mr Blair told Forbes magazine in an interview posted on its website last week.
"My own judgment is that provided we handle it with care, there is a way through which meets America's objectives and other people's concerns," he said.
'Bond of kinship'
Mr Blair's official spokesman, Alastair Campbell, said the meeting of the two leaders was unlikely to produce a more concrete response, because US plans had yet to be formalised.
He also played down British fears that the shield would involve basing American missiles in Britain.
The prime minister maintains nothing will dent relations between Britain and the United States.
Earlier this month he said the two nations shared "bonds of kinship and history and a bond of a shared language, but most of all ... shared values".
Trade is likely to be another sticking point during his US trip.
While US-British trade has doubled in the last decade - from £38bn ($55 bn) to £76bn ($110bn) annually - Washington and the European Union are embroiled in several long-standing disputes.
This includes a decade-long trade war over bananas.
Mr Campbell said Mr Blair would press for a new round of world trade talks later this year.
"The 2% of trans-Atlantic trade that's mired in dispute has been allowed to poison relations for too long," said Mr Campbell.