The plane is reported to have belonged to an aviation firm owned by the family of the former al-Qaeda leader.
The Saudi embassy in the UK has issued a statement offering condolences to the family, without confirming the identities of those killed.
The statement, on Twitter, said the Saudi ambassador to Britain, Prince Mohammed bin Nawaf bin Abdul Aziz, had paid his condolences to the family and relatives of Mohamed Bin Laden.
It added that the embassy would be following up the incident and its circumstances with the responsible British authorities, and that it would work on the transfer of the bodies of the victims so that funeral prayers and burials could take place in Saudi Arabia.
The plane, which was arriving from Milan, Italy, crashed into a British Car Auctions site at the airfield shortly after 15:00 GMT, exploding on impact.
Its pilot and all three passengers were killed but no-one on the ground was injured, Hampshire Constabulary said.
In a statement, Blackbushe Airport said the jet had crashed near the end of the runway while attempting to make a landing.
A spokeswoman for Milan Malpensa Airport confirmed the plane had left at 13:30 BST on its way to Hampshire.
The Saudi General Authority of Civil Aviation tweeted that the plane was a Saudi-registered private aircraft, and said it would support the UK`s Air Accidents Investigation Branch (AAIB) in its investigation.
Hampshire police are carrying out a joint investigation with the AAIB.
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