The Prime Minister is to meet the US President on Tuesday for talks at the United Nations General Assembly in New York, where he will also meet key EU leaders and Iran's President Hassan Rouhani.
The man-made climate crisis is a thorny subject with Mr Trump - who has dismissed it as a "hoax" and will reportedly miss the key summit in favour of a meeting on religious freedom.
But Mr Johnson said he would stress the importance of tackling environmental destruction and of not allowing the NHS to be available to the US when negotiating a free trade deal.
"I will be making the point to President Trump, a point that I've made many times before, that we must tackle climate change together and we must tackle the loss of species together," the PM told reporters on the plane.
"But I will also be saying to president Trump is that when we do a free trade deal we must make sure that the NHS is not on the table, that we do not in any way prejudice or jeopardise our standards of animal welfare or food hygiene in the course of that deal. And that we open up American markets."
The PM will discuss Brexit with Angela Merkel, Emmanuel Macron, Leo Varadkar and Donald Tusk. Climate change and tension in the Middle East will also be high on the agenda.
RAF Voyager landed in New York on Sunday evening - the early hours of Monday UK time - carrying with it Mr Johnson and assorted members of the media.
With the PM staying in the US until Wednesday, he could be out of the UK when the Supreme Court announces its decision on the legality of his prorogation of Parliament as Brexit beckons.
The UN is holding its Climate Action Summit, and Mr Johnson is set to announce environmental policies over two speeches.
Scientists will be able to use up to £1 billion of the aid budget inventing new technology to tackle the climate crisis in developing countries, under a clean energy fund named in honour of British physicist and suffragette Hertha Ayrton.
A further £220 million from the overseas aid budget will be used in efforts to save endangered species from extinction in an international biodiversity fund.
But brokering a new EU departure deal will be high on the PM's list of priorities, with the October 31 deadline looming.
He is expected to talk Brexit and the attacks on the Aramco oil facilities in Saudi Arabia in a meeting with French President Mr Macron and German Chancellor Mrs Merkel on Monday.
That will follow talks with European Council president Mr Tusk, who will have already met Mr Macron and Mrs Merkel.
He will go on to meet his Irish counterpart Leo Varadkar and Mr Trump separately on Tuesday.
Mr Varadkar's deputy, Simon Coveney, has said a "wide gap" remains between Mr Johnson and the EU in seeking a fresh deal.
The meeting with Mr Rouhani will come shortly after the PM accused Iran of being behind the attacks on oil facilities in Saudi Arabia.
The PM's partner, Carrie Symonds, is also expected to attend the General Assembly.
But a senior Government official stressed she was travelling for her own work with environmental group Oceana and not with the PM.
Other bilateral meetings anticipated for the PM are with Turkey's President Recep Tayyip Erdogan, Indian PM Narendra Modi, Egypt's President Abdel Fattah el-Sisi, Ukraine's President Volodymyr Zelensky, Jordan's King Abdullah II and UN Secretary-General Antonio Guterres.