Rincon suffered a severe head injury following a collision on Monday between the vehicle he was travelling in and a bus in the southwest city of Cali.
The former Real Madrid and Napoli ace underwent almost three hours of surgery before being transferred to intensive care, but died on Wednesday.
“Despite all the efforts made by our medical and care team, the patient Freddy Eusebio Rincon Valencia has died today,” said the Imbanaco Clinic in Cali, which was treating him.
“We ask everyone to honor and praise the life of Freddy Eusebio for all the joys he gave us,” clinic director Laureano Quintero said, his voice breaking, after reading the official statement.
Colombia’s football federation, the FCF, said his death was “a great loss” and “we will miss him and remember him with great affection, appreciation, respect and admiration.”
“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,” it said in a statement.
Rincon was born in the southwestern port city of Buenaventura and was known as the “Colossus” during his career.
He was a star of the Colombia side that played at the World Cup in Italy in 1990 and also featured at two more World Cups.
‘A great idol’
Rincon spent much of his career in Brazil, turning out for Palmeiras and Corinthians, where he won the FIFA Club World Cup in 2000.
“It is with great sadness that we say goodbye to a great idol. Our captain in the first world title, Freddy Rincon, passed away in the early hours,” Corinthians tweeted with a photo of Rincon.
“Eternally in our hearts.”
World football’s governing body FIFA expressed “sincere condolences” to Rincon’s “loved ones, former teammates and fans from the clubs he played for.”
Rincon was part of a talented Colombian team that qualified for the 1990 World Cup finals, ending their 28-year absence from football’s most prestigious tournament.
He is particularly remembered for a last-minute goal in their 1-1 draw against powerful West Germany, the eventual World Cup winners.
Rincon started his career in the 1980s with Santa Fe and America de Cali before joining Brazilian club Palmeiras.
He also had a stint with Napoli and then joined Real Madrid.
Rincon spent only one season at the Bernabeu and in a 2012 interview with the Spanish daily Marca spoke of the “very marked racism” he had suffered at Real Madrid.
He hung up his boots in 2004 after a final season with the Corinthians.
The midfielder was previously involved in a serious traffic accident in 2013 in which he suffered several fractures and a head injury.
After Monday’s fatal accident, local media broadcast a video in which a van is seen crossing an intersection when a bus hits it on the passenger side.
In these images “it seems that the traffic light is red when the van crosses and there could also have been speeding” by the van or the bus, according to the Cali mayor’s office.
Rincon’s companions had said he was at the wheel, according to an initial assessment by the authorities.
The mayor’s office, however, said on Tuesday that only the attorney general’s office “will be in charge of determining the identity of the driver of the vehicle.”