The 64-year-old Briton told the International Automobile Federation's general assembly at a meeting in Paris of his surprise decision to quit a year before he would have been up for re-election.
He was due to hold a news conference at Magny-Cours on Friday, where Formula One teams were preparing for Sunday's French Grand Prix.
"I'm very surprised about the news," said team boss Eddie Jordan. "It's a difficult time in Formula One and I hope he will look at the whole matter again and perhaps reconsider."
Ferrari's six times world champion Michael Schumacher expressed his sense of shock.
"Obviously that's quite surprising news," he said. "I think Max has been very good in what he has been doing.
"There have been maybe times I haven't agreed with him but in general for the sport I think he has achieved a lot in terms of safety and the reputation of Formula One. He has been very active and a hard worker.
"It will be interesting to see who will replace him, whether we are going to have an improvement or not, but it will be difficult to replace Max in my view."
CONTROVERSIAL CHANGE
The FIA groups together the motoring clubs of 119 countries and oversees several world championships, including world rallying, and more than 600 international motor sport competitions.
Mosley's tenure was due to end in October 2005 although he had intimated previously that he was interested in another term in office.
He has been embroiled recently in controversial changes proposed for both the Formula One and world rally championships, vowing to force through measures to make grand prix racing safer, cheaper and more competitive.
Mosley said on Wednesday, at which he gave no hint about quitting, that he was confident important changes would be pushed through on safety grounds by October to come into force for 2005.
The two line FIA announcement gave no reason for his decision to stand down and there was considerable speculation in Formula One circles about the motives, although some suggested that he had simply had enough.
There was no immediately obvious choice of successor, although French Federation head Jacques Regis had been tipped as a possible challenger while Ferrari boss Jean Todt had been mentioned by Mosley himself.
Mosley first became FIA president in 1993 on a four-year term and was re-elected in 1997 and 2001 to lead an organisation celebrating its centenary this year.
The suave and aristocratic barrister has for decades been close to Bernie Ecclestone, Formula One's commercial supremo, and his departure will be seen as the end of a formidable double-act.
Son of the British pre-war Fascist leader Oswald Mosley and Diana Mitford, Mosley was an amateur Formula Two driver and later co-founded the March Formula One team.
