The American company, who joined the grand prix scene in 1965, will withdraw at the end of 1998, blaming next season's rule changes. Goodyear, whose British base is in Wolverhampton, supply tyres to all of Formula One's main teams, including Ferrari, McLaren, Benetton, Jordan and Williams, the constructors' champions.
After Goodyear's withdrawal, those teams are expected to switch to Bridgestone - who ended Goodyear's six-year monopoly of Formula One last season - although another company, Michelin, may return to Formula One.
Last season, Goodyear tyres won every race, taking the number of wins to 361 to give Goodyear a 25th drivers' crown and 26th manufacturers' title.
"We will miss their expertise, but will keep their chair warm in case they return," Frank Williams, the head of Williams, said. "Goodyear are our longest- standing technical partner and we are very proud to record that 99 of our 103 wins have been on Goodyear rubber."
Claudio Berro, the Ferrari spokesman, said: "We regret that such a major company are leaving Formula One. And we didn't expect it. There was absolutely no warning."
Another team chief, Eddie Jordan, described Goodyear as being "probably the longest serving and most supportive company ever in Formula One."
William Sharp, the president of Goodyear's global support operations, confirmed that they would still develop the new grooved tyres which are being introduced in the sport next year.
They were pulling out because of the "rule changes imposed for race tyres in 1998, the ever-escalating cost of participation and the consequent diminishing return on the company's investment."
Sharp added: "We saw our participation in Formula One racing as an investment in R and D [research and development] to provide Goodyear customers with hi-tech products. It has now become clear that this investment must be redeployed."