Byrne was termed "the Babe Ruth of insurance" by Warren Buffett and was renowned for being the best in the business at buying and turning around ailing firms.
He was introduced to the "Insurance Hall of Fame" in 2009 while being described as "truly unparalleled in the insurance industry".
He saved Geico from bankruptcy in the 1970s and Buffett was so impressed he later brought the whole firm.
In the 1980s Byrne was hired to rescue Fireman's Fund from financial ruin and by 1985 it was floated in the largest initial public offering (IPO) of the time, and sold to Allianz in 1991 for $2.9bn.
Byrne held onto the holding company, though, initially named Fund American and later changed to White Mountains Insurance Group.
Byrne trained as an actuary and began his career at his father's insurance agency in New Jersey. He then joined Lincoln National Life Insurance Company in 1959 as a reinsurance salesman and assistant manager.
He went on to work for The Massachusetts Life Insurance Company and Travelers Insurance Company, where he was appointed executive vice-president, overseeing the life and personal lines divisions.
In 2011, Reactions as part of our 30th anniversary celebrations named Byrne sixth on our list of most influential people since Reactions was launched. We also spoke to Byrne for a retrospective on how the industry had changed.
Byrne, whose career of turning around struggling companies such as Geico and Fireman's Fund is the stuff of industry legend, told us the biggest change in the commercial property/casualty market in the past three decades is all of the firms that went out of business and got replaced.
"In 1980 there were an awful lot of companies around that aren't around anymore," Byrne, who retired from White Mountains in 2007, told us. "The Aetna, USF&G, the Continental, the Home, Reliance, St Paul - all gone. I don't mean they all went insolvent, but they got recapitalised or merged under great capital tension. I lived through those 1980s and 1990s and in a sense Mr Buffett and I made a business out of trying to help those companies."