Matthew Daley, 35, killed Donald Lock, on the A24 in Findon, near Worthing, last July after the 79-year-old ran into the back of his vehicle.
He was convicted of manslaughter after he admitted stabbing Mr Lock to death, claiming diminished responsibility.
Daley was told he would initially serve his time in a secure mental hospital.
Lewes Crown Court heard Daley was a paranoid schizophrenic whose mother, Lynda, had pleaded with mental health experts to have him sectioned.
She told the court the day she heard Mr Lock had been killed was "the day that all your nightmares came true".
Daley was charged with murder, but never denied killing Mr Lock on 16 July last year.
Daley will be held in Hellingly medium-secure psychiatric hospital in East Sussex under the Mental Health Act.
Should his health improve, he will then be transferred to prison.
Mr Justice Singh said the killing was a "violent, unprovoked attack" in front of members of the public, aggravated partly by Mr Lock's age and the use of a weapon.
"It's clear from the verdict that the defendant's responsibility for the homicide was substantially impaired," he said.
"It does not follow that it was completely extinguished."
Prior to the start of the trial, Sussex Partnership NHS Foundation Trust apologised for not doing more.
It has since announced an independent review into 10 killings involving patients known to the Trust, including the case of Matthew Daley.
Mr Lock's son Andrew said the sentencing of Daley did not did not remove from the family's memories the horror of what happened.
"However, at least we can move on knowing that the public are properly protected from a man who, whilst badly treated by the NHS by a catalogue of failures, is a danger to the public if not properly supervised and medicated," he said.
"It is important to note Mr Justice Singh's observation this was not a public inquiry into the failings of the NHS.
"But it is now up to the NHS that the systematic arrogance that exists in the medical world changes for good and that they wake up to the fact that we all deserve to be listened to."
A man who stabbed a retired solicitor 39 times after a crash between their cars has been given life and will serve at least 10 years.