Boom Supersonic expects a prototype of its passenger plane to make its first test flight by the end of 2018.
Subsonic and supersonic tests will take place in the US.
If the full-size 55-seat plane is then approved, the first passengers could be travelling at supersonic speeds across the Atlantic by 2023.
Rolls-Royce warns against 'hard Brexit'
Boeing launches new version of 737 jet
Airbus unveils upgraded A380 jumbo
Blake Scholl, the founder and chief executive of Boom, said at the Paris air show that the design of the XB-1 demonstration plane had passed a performance and safety review ahead of manufacturing.
Boom said five unnamed airlines had placed 76 orders for its passenger plane, which resembles Concorde but has a delta wing that sweeps almost to the tip of the nose.
It will also ditch the afterburner engine used by the British-French supersonic pioneer that was not only extremely loud but also very thirsty.
"By using a modern turbofan engine like Boeing and Airbus, you can make the aircraft both quieter and significantly more fuel efficient," Mr Scholl told the BBC.
The company claims that airlines flying its plane will be able to charge similar prices to a business class fare on the lucrative London-New York route of about $5,000 return.
Concorde tickets used to cost up to about three times that amount.
Time-poor travellers, meanwhile, will jump at the chance of getting to or from those two cities in about half the time a subsonic plane takes, according to Boom.
"Airlines are excited for something new and different to offer their passengers," Mr Scholl said.
Although Concorde had the backing of both the British and French governments, he said it was not economic because the imperative then was to beat the Soviet Union into the supersonic age, rather than build a practical or affordable plane.
"Being a private company that has to raise investment means we have to have a business case that is profitable for airlines and affordable for customers," Mr Scholl said.
Although many remain sceptical that Boom can deliver its promises, the company said in March that it had raised the $33m that would allow it to build and fly the demonstration plane.
One believer in the project is Virgin founder Sir Richard Branson, who announced late last year that he planned to buy the first 10 passenger jets made by Boom.
His Virgin Galactic space travel venture will also provide manufacturing and engineering services, as well as flight test support.

Doctors had said Ontlametse Phalatse would not make it past the age of 14.
President Jacob Zuma was among those who conveyed their condolences to the family of "the special child of South Africa". She was known as the "First Lady" by her friends and family.
Local broadcaster Enca called her the country's "champion of positivity".
Africa Live: More updates on this and other stories
In a tribute her family wrote: "We will miss you sorely, Tsontso, our first lady. May you find eternal peace among the angels. Rest in Peace".
She called herself the first lady because she was the first black woman in South Africa to be diagnosed with progeria.
Ontlametse loved life, lived it to the full, and never wished that she was born in any other way.
This is what South Africans will remember her for.
She rose to prominence a few years ago when a documentary was made of her life.
Ms Phalatse used her new-found fame to motivate people to get on with their lives. In the process, she touched the hearts of many South Africans.
The country got to share in some of her special moments and milestones - her 16th birthday, a school graduation ball and more recently her 18th birthday party spent with President Jacob Zuma.
Ontlametse died surrounded by her family, who described her as having a "courageous spirit". Her legacy at 18 is not taking life's precious moments for granted.
President Zuma led a minute's silence for Ms Phalatse on his 75th birthday and said he had planned to give her a car.
"A brave young fighter has fallen. May her spirit inspire all others living with disabilities or facing any difficulty, to soldier on as she did and live life to the fullest. We are really proud of her," he said in a statement.
Sources: Medical News Today, US National Library of Medicine, Mayo Clinic
Supersonic air travel could be back in little more than five years if a plane that aims to replace Concorde takes to the skies.
[NEXT_CONCEPT]
A woman who captured the hearts of many South Africans for her brave battle against premature aging disorder progeria has died aged 18.