Watkins, who was 84, spent 26 years in his role - transforming safety standards in F1 and continuing his efforts as part of the FIA Institute even after he stood down from his full time position at the end of 2004.
The impact that Watkins had on the sport was never underestimated – and team chiefs and drivers were all keen to pay their tributes to the great man.
JEAN TODT, FIA PRESIDENT
"This is a truly sad day for the FIA family and the entire motor sport community. Sid was loved and respected in equal measure by all those who knew and worked with him. We will always be grateful for the safety legacy that he has left our sport."
FORMER MCLAREN TEAM BOSS RON DENNIS
"Today the world of motor racing lost one of its true greats: Professor Sid Watkins. No, he wasn't a driver; no, he wasn't an engineer; no, he wasn't a designer. He was a doctor, and it's probably fair to say that he did more than anyone, over many years, to make Formula 1 as safe as it is today.
"As such, many drivers and ex-drivers owe their lives to his careful and expert work, which resulted in the massive advances in safety levels that today's drivers possibly take for granted. But, more than that, Sid was a dear friend of mine, and I'll miss him bitterly.
"To his widow Susan, and to his family, I extend my sincerest condolences. He was a truly great man, and the world of motor racing simply won't be the same without him."
MARTIN BRUNDLE ON TWITTER
Motor sport has lost a true visionary +character with death of Prof Sid Watkins, 84. Great man, funny too. Saved my left foot being amputated.
Sid W would often prescribe 'a stiff whisky and aspirin' unless your leg was hanging off. His way of saying 'just put up and get on with it.'
Sid was the 'go to' man for health in Motorsport. He helped, saved, or made more comfortable, numerous people who never sat in a racing car.
RUBENS BARRICHELLO ON TWITTER
It was Sid Watkins that saved my life in Imola 94. Great guy to be with, always happy...tks for everything u have done for us drivers. RIP
JENSON BUTTON ON TWITTER
Rest in Peace Sid Watkins...Motorsport wouldn't be what it is today without u. Thank you for all you've done, we as drivers are so grateful.
"Only a life lived for others is a life worthwhile." ~Albert Einstein. RIP Professor Sid Watkins.
HEIKKI KOVALAINEN ON TWITTER
Sad to hear professor Sid Watkins has past away, one of the true greats in motorsport. R.I.P
LEWIS HAMILTON ON TWITTER
It's a sad day, with the loss of professor Sid Watkins. Without his incredible contribution to the sport, our lives as drivers would be a risk. My condolences go out to his family.
Sid Watkins was one of the best Men I have met in my life, totally selfless and the world has lost a great man.
FAMILY STATEMENT OF GRATITUDE
In light of the outpouring of emotion, Watkins' family issued a statement on Thursday expressing their gratitude for all that has been said.
It was also announced that a memorial service will be held in the next few months.
The statement said: "Professor Sid Watkins, Formula 1 doctor and leading neurosurgeon, died peacefully in a London hospital lat night aged 84, after a short illness.
"His family would like to thank everyone for the many messages of support and the touching tributes from the world of motor racing, medicine and beyond.
"There will be a private family funeral in Scotland followed by a memorial service in London in the coming months, details of which will be announced shortly."