In her first foreign trip as Prime Minister, Ms Truss was flying overnight to the States for the annual United Nations General Assembly (Unga).
The visit will contain a series of meetings, including with the EU’s Ursula von der Leyen, and a speech to world leaders. It comes as political action resumes after the period of national mourning for the Queen.
Ms Truss hopes the focus will be largely on energy security and combating Russia’s war in Ukraine, but clashes over the Northern Ireland Protocol are bound to feature.
Mr Biden, the US President with proud Irish heritage, has raised concerns about Brexit’s threat to the peace process and has downplayed the chances of striking a free-trade deal.
His French counterpart, Mr Macron, has long been a critic of Brexit and has been firm in pressing the UK to keep to commitments on Northern Ireland and fishing rights.
Ms Truss sparked a diplomatic row during the Tory leadership contest when she declined to give a clear answer when asked if the president of the allied nation was a “friend or foe”.
Instead, the then-foreign secretary said last month that the “jury’s out”.
Ahead of the visit the Prime Minister’s spokesman described France as a “longstanding ally” and insisted relations between London and Paris, as well as with the EU, are “good”.
Asked if the meeting with Mr Macron will be uncomfortable, the spokesman said: “No, the Prime Minister wants to build a constructive relationship with President Macron.”
But the spokesman maintained the position on the controversial Northern Ireland Protocol Bill, which the EU and others say will break international law.
Ms Truss will meet Mr Macron on Tuesday, before seeing Mr Biden on Wednesday. She had been set to talk to the US President in Britain over the weekend as he visited for the Queen’s funeral, but the meeting was postponed.
She is not scheduled to receive the White House visit that Boris Johnson was treated to during his visit to Unga last year.
Meetings with the leaders of Turkey, Spain and Israel are also expected, and Ms Truss will warn that now is not the time to “take our foot off the gas” in opposing Vladimir Putin’s invasion of Ukraine.
Before leaving the States on Wednesday evening, Ms Truss will use her summit speech to say the UK under her leadership will be “an active defender of our democratic values” and will work to counter authoritarianism with allies.
The trip kicks off a frantic few days of political action in Ms Truss’s fledgling premiership, with details on how businesses will be helped through the energy crisis and a major announcement on the NHS billed.
Ms Truss, who was being joined by Foreign Secretary James Cleverly in the US, will then return ahead of Chancellor Kwasi Kwarteng’s mini-budget on Friday.