The pair first met in 2009 when they flew a 1955 Super Constellation from Sydney along the coast of NSW.
Mr De La Hunty is the president and founder of the Historic Aircraft Restoration Society (HARS) and saved the Constellation from an American aviation graveyard in a labour of love that cost millions of dollars.
"We share a mutual respect for old airplanes and flying and at that stage we were keen to suggest to him that if he ever wanted to part with his Boeing 707 we would be very interested in it," Mr De La Hunty said.
"When we heard earlier this year that he was looking at possibly not continuing with his Boeing 707, we made contact.
"He jumped at the idea and so we've been in detailed discussions and negotiations since."
The plane was part of a delivery of 11 aircraft made to Qantas in 1964, the first jet aircraft in its fleet, and replaced the Lockheed Constellations on long distance flights.
After Travolta's Boeing 707 finished with Qantas, it flew for an American airline before it was acquired by a syndicate that included another show business celebrity, Frank Sinatra.
"We are all linked into this big history together," Mr De La Hunty said.
It is an important addition to the society's collection because it fills a gap between the Constellation and another historic Qantas jet in the society's burgeoning collection, the City of Canberra.
Hundreds of people gathered at the regional airport, south of NSW's Wollongong in NSW, to watch the arrival of the Canberra — the first 747-400 in the Qantas fleet.
The plane is the first of its type to be preserved for public display and gained the record in 1989 for the longest non-stop commercial flight between London and Sydney.
It is a record that still stands.
The exact timing of Travolta's 707 is still to be worked out but is unlikely to be for some months to come.
Although the plane last flew in December and is in relatively good condition it will need some engineering work, and the plane will not arrive without Travolta on board as a crew member.
"It's going to take a bit of time not only to coordinate the engineering, but it will also need the coordination with John and his movie commitments," Mr De La Hunty said.
Travolta released a statement over the weekend saying the plane needed work to be restored to a safe flying state, but he was confident that the HARS volunteers — many of them retired Qantas engineers — were up to the job.
"I am truly excited by this project and am just so pleased that this beautiful aircraft, for which I obviously have very fond memories, will continue to fly well into the future," the statement said.