Matthew Daley, 35, knifed 79-year-old Donald Lock 39 times on the A24 at Findon, near Worthing in West Sussex, on July 16 last year.
Daley stabbed Mr Lock after his Toyota crashed into the back of Daley’s Ford Fusion at about 16mph, causing minor damage to both cars.
Before the killing, Daley’s family had “pleaded” with clinicians to section him as his mental health declined, a trial heard.
At Lewes Crown Court, Daley was sentenced by judge Mr Justice Singh after he was convicted of manslaughter but cleared of murder in May.
The judge ruled that instead of being detained in jail, Daley will be held in Hellingly medium-secure psychiatric hospital in East Sussex under the Mental Health Act.
If and when it becomes no longer necessary, Daley will be transferred to prison to serve the remainder of the minimum term.
Sentencing Daley, the judge said: “It’s clear from the verdict that the defendant’s responsibility for the homicide was substantially impaired.
“It does not follow that it was completely extinguished.”
Days before the trial started, chiefs at Sussex Partnership NHS Foundation Trust apologised to Daley’s relatives for not doing more.
Mr Lock’s son Andrew Lock criticised the Trust after the trial, saying his father would still be alive if mental health teams had done their jobs properly.
Trust chief executive Colm Donaghy said “we got things wrong” and signalled changes would follow but he believed staff were not deliberately negligent.
Mr Lock would have turned 80 last week and a party had been planned by his widow before he was killed, his son added.
His voice trembling with emotion, at yesterday’s sentencing he told how his father was enjoying his retirement cycling and following Brighton and Hove Albion FC before he died.
And added: “He was a real gentleman who loved life.”
The shunt happened after Mr Lock, who was returning from a cycling meeting, had to brake suddenly after Daley inexplicably made an emergency stop.
Following the crash, a “calm” Mr Lock got out of his car to ask Daley why he had braked suddenly. Daley then launched his knife attack. Mr Lock, who had recently been given the all-clear from prostate cancer and was to become a great-grandfather for a sixth time, died at the scene.
The two-week trial heard University of Portsmouth architecture graduate Daley had suffered mental illness for ten years, and his family had “pleaded” with experts to section him.
His mother Lynda Daley told jurors he was never given a proper diagnosis.