Close became the youngest player ever to win a Test cap for England when he made his debut against New Zealand in 1949 as an 18-year-old.
The famously brave batsman went on to lead his country seven times in 22 Tests, and also captained his native county to win four County Championship titles.
Yorkshire captain Andrew Gale, speaking before his side's County Championship game at Hampshire, which started this morning, said: "He was a legend, and it's a sad day for everyone at Headingley.
"He was around throughout my career and was an inspiration to us all, we are proud to have won back-to-back Championship titles but today is a sad day for Yorkshire cricket and this gives us a bit of extra motivation to go and win this game, for Brian."
A statement on Yorkshire's website read: "It is with the deepest regret that Yorkshire County Cricket Club announce the death of Brian Close, CBE, one of Yorkshire and England’s greatest ever captains and one of the game’s most courageous players.
"In addition to his outstanding cricket career, Brian remained fully committed to Yorkshire until the end, being a Life Member of the club and President from 2008-2010. He was also a popular former President of the Yorkshire CCC Players’ Association.
"He leaves a widow, Vivienne, and a son and a daughter."
Dickie Bird, who played for Yorkshire with Close, said: "He will have been over the moon to see us win back-to-back Championship titles. I remember Brian in the dressing room with a cup of tea, Sporting Life on the table and a cigarette on. He was as happy as a sandboy.
"As a player, and as a captain, he was as brave as anybody; he stood up to everyone, and was scared of no-one, whether batting or fielding at short-leg.
"He played a big role in the development of Viv Richards and Ian Botham, too, so they owe Brian a big debt of gratitude. He will be sadly missed."