Tributes have flowed for the 72-year-old who has been remembered as a compassionate and humble man and someone highly respected for his leadership.
Mr White died at the scene following a collision involving a vehicle in Adelaide's inner southeast on Sunday morning.
Police and ambulance crews were called to an intersection at Glen Osmond shortly before 10.30am following reports of the crash.
A 61-year-old man behind the wheel of the vehicle was on Sunday afternoon assisting with investigations.
His car was towed away for examination, police said.
Mr White's death was confirmed "with great sadness" by acting NT Police Commissioner Murray Smalpage.
While SA Commissioner Grant Stevens said the death came in "tragic circumstances".
"Paul was highly respected by both SA Police and the NT Police and will be remembered for his leadership, both in policing and right across the community," Mr Stevens said.
"Paul had many close friends amongst current and retired police officers in SAPOL and will be sadly missed."
Mr White retired from the NT force in 2009, following almost eight years as top cop.
He joined SA Police as a cadet in 1968 and rose through the ranks to the position of assistant commissioner before his departure.
In that role, he took charge of the state's crime command and was responsible for efforts to tackle bikie gangs.
SA Emergency Services Minister Joe Szakacs said the loss felt by the police community any time one of their current or former members passed was real and profound.
"My and the government's condolences are with Mr White's family, loved ones and the entire police fraternity," he said.
"He made an extraordinary contribution to policing, not just in South Australia but in the Northern Territory as well."
The Northern Territory Police Association said Mr White would be remembered as a compassionate and humble man.
"Anyone who knew Mr White certainly found him to be a really engaging commissioner," Acting president Owen Blackwell said.
"He always had the welfare of the troops at heart and he genuinely cared about his police force and a significant number of his policies were developed to ensure members were looked after."
Police said investigations into the crash were ongoing and asked for anyone who witnessed the incident or with dashcam footage to come forward.
