It could see flight times slashed in half – with a journey from London to Newark in New Jersey taking three and a half hours.
Currently, a flight between those two locations would take almost seven hours.
The record for the fastest flight by a commercial airline between New York and London is two hours, 52 minutes and 59 seconds – set by Concorde in 1996.
Concorde was retired from service in October 2003 after British Airways and Air France blamed a downturn in demand and increasing maintenance costs.
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The final Concorde departed three years after an Air France Concorde flight 4590 crashed into a hotel shortly after take-off from Paris – claiming the lives of 109 people on board and a further four people on the ground in 2000.
Mike Leskinen, United vice president of corporate development and a former aerospace analyst, said the Boom jet will be 75% cheaper to operate than the Concorde – thanks to advancements in engines and lighter fuselages.
Those savings could make it possible for United to offer both premium and economy seating – although no final decision has been made about cabin layouts, Mr Leskinen said.
The 88-seat plane will be the first supersonic airliner to have zero carbon emissions by running on “pure sustainable aviation fuel”, United said.
A prototype is set to make its first journey through the skies this year or in early 2022.
Flight trials are scheduled to begin in 2026, in the hope passengers will be carried on commercial flights in 2029.
The company has declined to discuss any financial details however an executive said a deposit had been put down.
The deal includes an option for an additional 35 planes.
United chief executive, Scott Kirby, said: “United continues on its trajectory to build a more innovative, sustainable airline and today’s advancements in technology are making it more viable for that to include supersonic planes.
“Our mission has always been about connecting people and now, working with Boom, we’ll be able to do that on an even greater scale.”
Meanwhile Boom Supersonic founder and chief executive, Blake Scholl, described the agreement as a “significant step” to “create a more accessible world”.