Shortly after 6.15pm, two motorcyclists were involved in a collision with a horse on the westbound carriageway at Picket Post.
One of the riders, a 31-year-old man from Bournemouth, was taken by ambulance to Bournemouth Hospital where he was later pronounced dead.
The other rider, a 47-year-old man from Broadstone, was taken by ambulance to Southampton General Hospital with serious, but not life threatening, injuries where he remains.
The horse died at the scene.
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Both riders had been held in a queue of traffic while police initially responded to reports of a horse loose on the carriageway.
Officers were advising motorists to proceed with caution regarding the possibility of animals in the carriageway.
This element of the incident has been referred by Hampshire Constabulary to the Independent Police Complaints Commission and they are awaiting its decision on how this will be investigating.
Superintendent Chris Brown said: "This was a very tragic incident, and our thoughts today are with the family of the motorcyclist who died and with the motorcyclist who remains in hospital.
"We understand how difficult and frustrating it can be to be stuck in traffic whilst incidents such as this are dealt with, and we would like to thank motorists for their patience while we responded to the incident which involved a comprehensive investigation and an extremely complex scene.
"The decision to close a road, particularly a main road such as the A31, is never taken lightly, and I appreciate the disruption this caused. We sent all available officers to the scene swiftly, and they worked hard to get the scene moving as soon as possible, including turning vehicles round and providing police-led relief diversions.
“We also took the very unusual step of re-opening a lane of the carriageway many hours before the road fully re-opened, whilst keeping the other lanes closed in order to conduct a full road death investigation. This decision was made purely to get traffic flowing, ease congestion and help frustrated motorists progress on their journey.
“This was a very complicated scene. We were dealing with what looked at the time to be a potential double fatal and the death of a horse on a main road, all of which has to be recovered with great care and diligence, and the scene forensically examined.
“The reality is that it is unavoidably time consuming, and the logistics and geography of this part of the A31 meant that the consequent impact to that road and the motorists that use it are huge.
“Our officers at the scene were 100 per cent focussed on clearing the scene as swiftly as possible. Road death investigations are by their nature very thorough and detailed, to prepare a file for any potential criminal proceedings, a file for the coroner, and vitally, we owe that as a duty of care to the family of the victim.
“Road traffic alerts were quickly issued on local radio detailing the road closure, and social media was updated, but at that time on a week night, a large volume of traffic is always going to be caught up in the area and unable to avoid the tailbacks.
“We will look to see whether there are any other methods we can use to enhance our system of communicating with drivers caught up in such tailbacks outside of conventional media.
“Our investigation continues, and we would ask anyone with information about this collision and who has not yet spoken to us, to please contact us now.”
Anyone with information about the collision is asked to contact the Road Death Investigation team at Eastleigh, quoting Operation Hedingham, on 101.