Two other cars were involved in the incident apart from ambulance.
Police will not give further details at this stage and will not identify the people involved for at least 24 hours.
South Central Ambulance Service have released this statement:
"A double crewed ambulance belonging to South Central Ambulance Service NHS Foundation Trust was involved in a collision with a tree on the A337 Brockenhurst to Lyndhurst road at 09.35 this morning.
"The ambulance was en route to Southampton General Hospital at the time of theincident conveying an elderly male patient. The patient was accompanied in theambulance by a relative.
"A female member of the ambulance crew and the elderly male patient were pronounced dead at scene.
"A male relative of the deceased patient was collared and boarded at scene and has been conveyed to Southampton General Hospital by land ambulance.
"A male ambulance crew member has been airlifted to Southampton General Hospital by the Hampshire and Isle of Wight Air Ambulance (Helimed 56).
"South Central Ambulance Service NHS Foundation Trust is conducting appropriate welfare checks with the families of all involved.
"The road is closed until further notice and motorists are asked to avoid the area. Diversions are in place."
A337 in both directions closed due to accident investigation work between B3055 Balmer Lawn Road (Brockenhurst) and Beechen Lane (Lyndhurst). Expect delays.
The road is expected to remain closed until this afternoon for investigation works and recovery. Diversion - a lengthy diversion via the A35.
Gwyn Williams was over taken by the ambulance shortly before the crash in the New Forest and told ITV Meridian what he saw.
He had been driving along the A336 between Brockenhurst and Lyndhurst in the New Forrest.
A 20-year-old man has been arrested at the scene of a fatal crash in which an ambulance crashed into a tree in the New Forest. The driver of the ambulance and the patient were killed. The two other occupants of the ambulance are in hospital with serious injuries.
The 20-year-old man - who was not on board the ambulance - has been detained on suspicion of causing death by driving without due care and attention.
The incident happened on the Brockenhurst to Lyndhurst road, at 9.35am.
The A337 is expected to remain closed for the rest of the day while investigators examine the cause of the accident. Motorists are being asked to avoid the area. Diversions are in place.
Two people have died after a collision involving an ambulance on the A337. The vehicle went into a tree, for a reason that has yet to be established.
The driver of the ambulance; a female paramedic, and an elderly male patient travelling in the rear of the ambulance died at the scene.
A male crew member and a male relative of the patient, who were both travelling in the back of the ambulance, are being treated for serious injuries at Southampton General Hospital.
Hampshire Police are investigating. Witnesses are asked to contact the Road Death Investigation Team at Eastleigh on 101, quoting Operation Feldburg.
An ambulance has collided with a tree on the A337 in the New Forest. The incident happened at 9.35am on the Brockenhurst to Lyndhurst road, at its junction with New Park. Four people were on board at the time. Hampshire Police are at the scene. Diversions are in place.