The cash will “unleash the talent of British scientists” and innovators abroad to, for example, provide clean energy from solar power and new large-scale battery technology.
Other projects will include designing electric pressure cookers to replace firewood, helping major polluting-factories reduce their carbon emissions and making cooling systems more energy-efficient.
The aid money will also help design low-emission and electric vehicles to cut pollution and make transport systems cleaner and greener in developing countries.
The prime minister will also use his trip to New York to unveil a £220m fund to save endangered animals such as the black rhino, African elephant, snow leopard and Sumatran tiger from extinction.
“Britain is a nation of innovators,” Mr Johnson said, ahead of the UN’s climate action summit on Monday, the day before he addresses its general assembly for the first time.
“Our scientists have been at the forefront of technological advancement for generations, pioneering world-changing inventions like the jet engine, the television and the lightbulb.
“If we get this right, future generations will look back on climate change as a problem that we solved by determined global action and the prowess of technology.”
The summit will be addressed by Greta Thunberg, the teenage activist who sailed the Atlantic to minimise the environmental impact of the journey.
The government is convinced the £1bn fund will be within UK aid rules, although it will potentially benefit British firms who will strike agreements for their services.
He will meet Donald Trump, Angela Merkel and Emmanuel Macron, as well as Donald Tusk, the European Council president, and Leo Varadkar, the Irish prime minister, in the latest round of frantic diplomacy.
The trip will also be the first made by Carrie Symonds, Mr Johnson’s partner, who is attending the event in her role as an adviser to Oceana, an environmental pressure group.
Ms Symonds will be staying with the prime minister and the official delegation, however, and is likely to attend at least one function, No 10 said.
The £1bn fund will be named after Hertha Ayrton, a leading British scientist and suffragette whose pioneering work contributed to major scientific advancements at the turn of the 20th century, including in electricity.
Her research into the flow of water and air also inspired the Ayrton fan, which was used on the Western Front in the First World War to dispel poison gas from British soldiers in the trenches.
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