Those behind the project say that it will help provide a new chapter in space exploration.
When finished in 18 months' time, the facility will house Virgin Galactic's space tourism business and other firms working in the commercial space arena.
It will cost the New Mexico government almost $200m (£121m).
Steve Landeene, executive director of the New Mexico Spaceport Authority, said: "The future is here and we are not too far off a new age of space.
"It is not just about private astronauts going up, it is about bringing the cost structure down and about new medicines, solar power in space and the entire range of scientific benefits that can come from it."
Big space
Speaking to several hundred people who had made the journey to witness the event in scorching temperatures, New Mexico governor Bill Richardson said it was "gratifying to see Spaceport America finally become a reality".
Work will now start on a suitably space-age terminal and hangar building deigned by Foster and Partners to blend in with the desert scrubland here, while housing rocket-based spacecraft and all the safety hazards that entails.
A 3,000m (10,000-ft) runway will ensure that there is plenty of room on the tarmac for even the world's largest planes.
When finished, Virgin Galactic - which hopes to begin regular tourist flights into space not long after the spaceport is completed - will base its headquarters and operations here, providing much of the spaceport's business, though Spaceport America is keen to point out it will not solely rely on the company.
WhiteKnightTwo takes to the skies
To impress upon those gathered at the site just how within reach the commercial space-age now is, the star attraction of the ground-breaking event was to have been a fly-by of Virgin Galactic's WhiteKnightTwo aircraft. But much to the disappointment of the crowd, at last minute it was forced to turn back with technical difficulties.
Will Whitehorn, president of Virgin Galactic, explained the craft was still in the testing stage and as such safety was of paramount importance when dealing with any problem, minor or otherwise.
He insisted that the company would not put a definite timeline on when the commercial flights would begin but that all was on track with its development plans.
WhiteKnightTwo - the aircraft which carries SpaceShipTwo to a high altitude before it launches into space - is to be publicly unveiled at the Oshkosh airshow in Winsconsin in July, while SpaceShipTwo should begin test glides in December.
If all goes to plan, the inaugural flight should carry Sir Richard Branson, his family and spaceship designer Burt Rutan on a sub-orbital ride within two years.
They will be followed by a waiting list of 300 who have all ignored the current economic climate and are willing to pay about $200,000 for the privilege of experiencing six minutes of weightlessness during the two-hour flight.
Testing ground
The location of the spaceport was selected for its distance from any sizable populations - only the occasional ranch and the local rattlesnakes will know it is there.
But New Mexico brings other advantages. The state proudly boasts that it has about 350 days of sun each year, meaning that unlike Nasa at Cape Canaveral, weather should not often affect launches, and the spaceport's neighbour - the White Sands missile testing range - ensures the air space overhead is already a no-fly zone.
Virgin Galactic's Stephen Attenborough: The testing programme goes on
Governor Bill Richardson said he felt that the economic benefits of positioning the state at the forefront of the burgeoning commercial space sector would lead to developments on many levels for New Mexico and build on its rich history of aviation and spaceflight.
New Mexicans are proud of their role in helping to foster scientific advancement from Von Braun's work with the V2 and Redstone rockets, to nuclear power, and the many observatories that are based here.
At the ground-breaking event, Governor Richardson recalled that his predecessor Jack Campbell even wrote to John F Kennedy in the 1960s to point out New Mexico's potential for the then nascent space industry.
He doesn't want his state to miss the boat - or spaceship - a second time around.
Mecico building a new spaceport.
