Don Lock, 79, was involved in a "minor" shunt with another motorist who then stabbed him to death on the A24 at Findon, West Sussex, on Thursday night.
Mr Lock, a great-grandfather of five, had got out of his car and was knifed repeatedly by the other motorist, who then drove off.
Sussex Police, who had earlier warned the assailant was "extremely dangerous", said they have now arrested a 34-year-old man from Worthing on suspicion of murder.
The man was believed to have been detained by armed officers after they launched a raid on a road where homes cost upwards of £1 million next to an exclusive golf club.
The dramatic arrest was understood to have been made in the area of a private road which leads to the golf club and to a car park on the South Downs.
Police cordoned off part of the road where a dark-coloured rucksack was discovered on a grass verge.
Officers were seen in the area carrying plastic tubes which are often used to keep bladed weapons free from contamination before forensic examination.
The scene at Warren Road, Worthing, is less than two miles from where the attack took place, and leads to a wooded area alongside the two 18-hole courses at the club.
A Sussex Police spokesman later said detectives were "not looking for anyone else at this time" in connection with Mr Lock's death.
One theory detectives are thought to be examining is that the assailant was driving a classic car and may have been excessively angered by damage caused in the collision.
Mr Lock's family, paying tribute in a statement, said: "Don has been a keen cyclist since the age of 12 and had been an active member of the Worthing Excelsior Cycling Club since 1960.
"He was not your typical great grandfather and was still cycling up to 150 miles per week.
"He still holds the club record for the 24-hour time trial having remained unbeaten for 44 years.
"He was full of energy having recently been given the all clear from cancer.
"Not only was he passionate about cycling but he had also been supporting Brighton and Hove Albion since the 1940s and was a season ticket holder.
"He loved travelling the world with his wife Maureen and he adored his family.
"He and Maureen had just celebrated their 55th wedding anniversary.
"Don leaves son Andy, daughter Sandra, four grandchildren, and five great grandchildren with the sixth great grandchild due later this year.
"Don had lived in Worthing for 55 years and was a popular member of the community.
"He was hugely loved by his family and friends and could often be called upon for his cycling or travel advice. Words cannot describe how much he will be missed."
A tearful Mrs Lock, 77, visited the scene of the attack and said: "He was a wonderful husband for 55 years and it has to finish like this. He was just a wonderful husband."
Ashley Goodlad, Mr Lock's grandson, described the attacker as "sick" and said the loss had "torn my family apart with pain".
He wrote on Facebook: "He was the kindest, softest and most generous man you could ever wish to meet, its just so confusing right now just trying to work out an answer for why this has happened.
"This sick person has taken away the best grandad anyone could wish for.
"I still can't believe this is real. It has torn my family apart with pain."
Close family are also believed to have gathered at the £400,000 detached, 1960s-built home Mr and Mrs Lock shared.
'No chance to defend himself'
Detective Superintendent Adam Hibbert, of the Surrey and Sussex Major Crime Team who is leading a murder investigation, said before the arrest was announced: "Mr Lock was the victim of a frenzied attack that he had no chance to defend himself against."The attacker has then driven off but at this stage we have a limited description of his vehicle.
"We are looking for an extremely dangerous man and need the public's help to identify and arrest him urgently."
Police are still appealing for information from anyone who witnessed the crime.
Det Supt Hibbert said Mr Lock was stabbed repeatedly and the attacker would have been covered in blood.
He appealed for information about the attacker's vehicle which will have suffered damage to its rear end and may also have been bloodstained.
Some witnesses suggested the assailant's vehicle may have been a classic car, or another type of older vehicle.
A Sussex Police source said: "We believe the car behind bumped into the one in front and gave it a minor, rear-end shunt.
"Both chaps got out and the driver of the front car attacked the bloke in the second.
"He was stabbed more than once."
An air ambulance landed at the scene and paramedics carried out first aid on Mr Lock but he died at the roadside.
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