Rincon had been in intensive care after a violent collision with a bus in Cali, Colombia.
Laureano Quintero, head medic at the private clinic where he had been admitted, announced the retired footballer had died just before midnight last night local time.
The Imbanaco Clinic said in a statement: “Despite all the efforts of our medical team, the patient Freddy Eusebio Rincon Valencia has died today April 13.
“We deeply regret this outcome, and at the same time offer our most sincere condolences to relatives, friends, acquaintances and fans.
“There will never be a way to express what this really means to us and we invite the whole country to remember him with joy for everything he gave us in life with his sporting achievements.”
Mauricio Serna (L) and Freddy Rincon, from the Colombian national team
Reuters Photographer
Freddy Rincon in action for Colombia
Wiki Commons
Rincon played for Brazilian club Corinthians in his prime, after securing a move to Real Madrid.
He also played for Napoli in Italy, as well as Palmeiras and Santos in Brazil.
Rincon will be immortalised by his goal against West Germany in the 1990 World Cup.
The 55-year-old was left fighting for his life after a crash between the Ford Escape he was in and a bus whose driver suffered a broken leg.
He was the most seriously hurt of the four people in the car.
Colombian football has begun to pay tribute to their highly-rated midfielder.
Their Federation wrote: "The Colombian Football Federation deeply regrets the death of Freddy Eusebio Rincon Valencia, and sends a message of support and encouragement to his family, friends and relatives at this difficult time."