Taylor, who also worked for European football's governing body Uefa as general secretary and an executive director, is said to have taken ill recently and passed away today.
SFA president Campbell Ogilvie said he will be "dearly missed".
Mr Taylor worked at the SFA between 1999 and 2007 before moving to Switzerland to work with Uefa. He initially trained as a solicitor and also worked with the Scottish Development Agency to promote Scottish business overseas before joining the SFA.
"On behalf of his friends and former colleagues at the Scottish FA, and throughout Scottish football in general, I would to express our profound sadness at the tragic news of David's death," the president said in a statement on the SFA website.
"I would also wish to send our deepest condolences to his wife Cathy, and their children James and Alan, at this dreadful time.
"David was a solicitor to trade but it was his love of Scottish football and, in particular, the Scotland national team that stirred his passion during his tenure as chief executive.
"He was great company, had an astute business mind and a forward-thinking approach to the game that, allied to his patriotism as a member of the Scotland Supporters Club, helped take the Scottish FA forward administratively."
In 2011 Mr Taylor had to be resuscitated after collapsing during a football match between officials from Uefa and Fifa. Speaking after the incident he said he was saved by quick acting medics who used a defibrillator.
Celtic chief executive Peter Lawwell also paid tribute, saying: "David was a fine man, a personal friend of mine and someone who made a great contribution to the game of football in Scotland. He will be very sadly missed by everyone who knew him.
"On behalf of everyone at Celtic Football Club, I would like to extend our deepest condolences to David's family and friends at this very sad time."
Current SFA chief executive Stewart Regan wrote on Twitter: "So sorry to hear that my predecessor, David Taylor, has died today aged 60. A top bloke. Really feel for Cathy, James and Alan. RIP David."