The men, aged 22 and 23, were taken into police custody on Saturday 22 August after the body of Liam Potts was found in the River Tyne on 18 August.
The soldier had been reported missing three days before that on 15 August.
Mr Potts, who served with the Coldstream Guards, was last seen heading towards Wylam in Northumberland at around 12.20am on Saturday 15 August.
Before his disappearance, Northumbria Police had received a report of a disturbance and subsequent collision involving a vehicle and a group of pedestrians on the bridge.
Police arrested two men and then bailed them in connection with the report on Monday.
They have since been re-arrested on suspicion of manslaughter as detectives investigate whether the two incidents directly led to Mr Potts entering the water.
Police made clear Mr Potts was not in the vehicle involved in the collision, nor was he struck by it.
The force said when officers found Mr Potts’s body, they did not believe there to be any third-party involvement, but further inquiries prompted the manslaughter arrests.
A man and a woman, both in their 20s, suffered serious injuries in the collision.
The woman has been discharged while the man remains in hospital for further treatment.
‘Heart of soul of any room’
Northumbria Police, in conjunction with HM Coastguard, North of Tyne Mountain and Northumberland National Park Mountain Rescue teams, carried out searches for Mr Potts.
While no formal identification of the body has taken place, Mr Potts’s next-of-kin have been informed.
His family said he was the “heart of soul of any room”.
They said: “To our Liam. You may no longer be here beside us, but your presence will never be forgotten. Your family, friends and colleagues have all said the same thing, ‘once you met Pottsy, you could never forget him.’
“You really were the heart and soul of any room.”
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Senior investigating officer Detective Inspector Rachael Rutherford, of Northumbria Police, said: “The facts remain the same that Liam was on the bridge at the time of the collision, but he was not an occupant of the vehicle and was not struck by the vehicle.
“Inquiries have revealed that Liam, for reasons yet to be established, entered the water within minutes of the collision.
“We have therefore made the further re-arrests as we are looking to establish whether there is any link between the collision and Liam entering the water.”
