Five-time world champion Lewis Hamilton described Charlie Whiting as a pillar of Formula One and an icon of the sport.
Four-time champion Sebastian Vettel recalled the veteran race director being a "driver's man" and a diplomat.
Drivers, team bosses and fans expressed shock and dismay on hearing the 66-year-old Englishman, who had a connection to F1 dating back to 1977, had died in Melbourne from a pulmonary embolism on Thursday, three days before the season-opening Australian Grand Prix.
"I spoke to him yesterday and walked the track for the first couple of corners together with him," Vettel told a news conference that had been scheduled to officially open the first F1 racing weekend of the season. "It's difficult to grasp when somebody is just not there anymore."
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The news conference started instead with drivers praising Whiting's contribution to their sport.
"He's been sort of our man — the driver's man," Vettel said. "There's the regulations, then there's us — he was the middle man. His door was always open.
"He was a racer — just a very nice guy. All our thoughts, the whole family of Formula One, are with him."
The federation for international auto racing released news of Whiting's sudden death in a statement.
FIA President Jean Todt described Whiting as "a great race director, a central and inimitable figure in Formula One who embodied the ethics and spirit of this fantastic sport."
A pulmonary embolism is a blockage in the lung, usually caused by a blood clot.
Whiting began his F1 career in 1977 working at the Hesketh team and later moved to Bernie Eccelstone's Brabham team in the 1980s. He joined FIA in 1988 and became a race director in 1997.
"Formula One has lost a faithful friend and a charismatic ambassador in Charlie," Todt said in a statement. "All my thoughts, those of the FIA and entire motor sport community go out to his family, friends, and all Formula One lovers."
Whiting was active in making F1 a safer sport and was widely acknowledged as a calming influence.
F1 Motorsports managing director Ross Brawn said he was devastated after losing a long-time friend.
"I have known Charlie for all of my racing life. We worked as mechanics together, became friends and spent so much time together at race tracks across the world," he said. "It is a great loss not only for me personally but also the entire Formula 1 family."
The Red Bull Racing team said Formula One had "lost one of its most loyal and hard-working ambassadors."
"I am deeply saddened to hear the terrible news," Red Bull team principal Christian Horner said. "Charlie has played a key role in this sport and has been the referee and voice of reason as race director for many years.
"He was a man with great integrity who performed a difficult role in a balanced way. At heart, he was a racer with his origins stretching back to his time at Hesketh and the early days of Brabham."
Ferrari team principal Mattia Binotto praised Whiting's diplomatic presence in the high-speed sport.
"Charlie was a true professional and extremely knowledgeable, but more than that, he was a wonderful person who always treated everyone with respect," Binotto said. "A tireless and enlightened motorsport expert, he helped make F1 safer and better. He was a pillar of Formula 1. Our sport is diminished by his passing."