Robinson was left with a fractured collarbone and ribs, a punctured lung and a deep cut to his arm when he was in collision with the car during a bike ride with friends in West Yorkshire last year.
But the 84-year-old, who was the first Briton to win a Tour de France stage and still rides 80 miles a week, was back in the saddle just six weeks after the accident.
The collision happened on July 16 last year, less than a fortnight after the veteran road racer was one of the guests of honour when the Tour de France visited his home county of Yorkshire.
Robinson, who won his first Tour stage in 1958, was cycling with friends in Thornhill when the car pulled out in front of him, knocking him to the ground.
Developers admit planning breaches in construction of Leeds retirement flats
Met Office issues thunderstorms and torrential rain weather warning for Leeds as heatwave comes to abrupt end
Paedophile arrested at Leeds Bradford Airport after travelling from Ireland to meet ‘13-year-old girl’
Aasia Majeed: Police launch urgent appeal to trace Leeds mum missing with one-year-old child
Major new £85m build-to-rent Leeds city centre development to go ahead following approval
Today, law firm Leigh Day confirmed that Robinson had received a £15,000 settlement for the costs of his bike and his injuries.
Andrew Bradley, head of the cycling team at Leigh Day, said: “Cycling is Brian’s life and we are extremely pleased to have played a role in getting him back on his bike.
“It has also been an honour to have helped a legend of the cycling world in his legal claim.”
Robinson, from Mirfield, West Yorkshire, said: “I would have preferred that it had not happened but I have been pleasantly surprised by how this incident has been handled through my British Cycling membership.
“I have had a great medical once-over and I am obviously pleased with the compensation which has enabled me to get back on my bike as quickly as possible.”