Eyewitnesses reported seeing a huge plume of black smoke rising hundreds of feet in the air from the airport at around 3pm.
The plane, a Phenom 300 Jet, came down near the end of the runway before careering into the neighbouring British Car Auctions (BCA) site.
Images and videos from the scene showed a vicious fire, which quickly engulfed the stricken plane as well at least a dozen parked cars.
Inspector Olga Venner, from Hampshire Constabulary, confirmed the four fatalities shortly before 7pm and said the Farnborough-based Air Accidents Investigation Branch (AAIB) was investigating.
"We can confirm that there were four people on board, including the pilot, and sadly there were no survivors," said Insp Venner.
"No-one on the ground has been injured. We would urge anyone with any information, including pictures or videos, to contact 101 and ask for Operation Cale.
"We secured the scene and we have got investigators from the AAIB along with our own investigation officers. It's still very early days.
"We are looking to keep the investigation wide and we're interested in any information anybody has for us."
The AAIB investigation will be assisted by the Saudi General Authority of Civil Aviation, after it confirmed the plane was Saudi-registered.
The business jet was coming in from Italy, having departed from Milan Malpensa Airport at 1.30pm, it was later confirmed.
Backbushe Airport is a general aviation airport near Yateley, which has long hosted the BCA on the same site.
The plane, after colliding with a number of parked cars, finally came to a rest towards the centre of the compound where it burst into flames.
Eyewitness Sheraz Aslam, 31, from Reading and a regular BCA customer, said he had gone back to pick up a couple of cars when the crash happened.
"An announcement came through [that] we had to evacuate [the site]," he said.
"I didn't think much of it, I thought it was just a regular fire alarm or drill. You don't think a plane is going to come down.
"Then a load of staff ran in and it was then we realised something was going on. I was very, very close, maybe 30 or 40 yards away.
"I didn't hear anything. All of a sudden, the flames went really big. We could hear all the fuel tanks in the cars start to explode and there was a terrible smell.
"Then I noticed a bit of the wing sticking out. It was sticking up in the air, but the rest of the plane was completely destroyed and on fire. The flames were leaping really high in the air. It was horrendous.
"Some of the staff were really shaken up. One guy I saw was in a bad way, he had been in a car just a few yards away. He was very shaken."
- RSPCA cruelty statistics 20161:20
- Fleet Services temporary building opens0:44
- Inside Hart Leisure Centre1:41
- Aldershot Garrison PT's Passing Out1:49
- Yateley School's production of The Sound of Music1:57
- Soldiers' new accommodation arrives at Aldershot 2:08
- Michael Casey court0:05
- Victoria Road Aldershot0:31
- 'Love Rushmoor' app0:35
Another eyewitness, 70-year-old Daphne Knowles from Mytchett, spoke of the plane's "screaming engines" as it passed.
"I was in a field with the cattle and I heard an aircraft coming very, very fast from behind me," she said.
"The engines were screaming far too much and the aircraft was trying to land - I'm a glider pilot and I thought, 'It's far too low to ground'.
"Then there was a huge black cloud of smoke which went up. It appeared it tried to land at Blackbushe having travelled northwards."
In a statement, Blackbushe Airport said: "We can confirm that a Phenom 300 Jet with four persons on board crashed near the end of the runway around 3.09pm while attempting to make a landing.
"The scene was attended by Blackbushe Fire & Rescue within minutes, followed by Hampshire fire, police and ambulance units."