Wiltshire Police said the collision took place in Derry Hill, near Calne, at 3am.
The occupants of the house immediately called 999 and were evacuated while the fire service extinguished the blaze. Nobody inside the house was injured.
Superintendent Steve Cox, of Wiltshire Police, said: “This was an absolutely horrific collision on our roads in the early hours of this morning.
“All blue light services attended the scene and were met with devastating scenes after a vehicle travelling along the A4 collided with a house and caught on fire.
“All four occupants of the vehicle died at the scene. Their families have been informed and we are in the process of assigning each family with specialist trained officers.
“My thoughts and the thoughts of all at Wiltshire Police are with them all today.”
Police said the A4 and the A342 remain closed while investigation and recovery work is ongoing at the scene of the collision.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies