Docherty, who was known as ‘The Doc’, spent nine years as a player with Preston, and won 25 caps for Scotland.
He went on to manage 12 clubs – including Chelsea, Aston Villa and Derby – as well as a stint in charge of his country.
But he was best known for his five-year spell at Old Trafford, overseeing an FA Cup final win over Bob Paisley’s Liverpool in 1977.
Docherty died at his home in the north-west on Thursday.
A family spokesperson said in a statement: “Tommy passed away peacefully surrounded by his family at home. He was a much-loved husband, father and papa and will be terribly missed.
“We ask that our privacy be respected at this time. There will be no further comment.”
United added in a statement: “We are deeply saddened by the passing of Tommy Docherty, who led us to FA Cup victory in 1977 with a thrilling, attacking team in the best traditions of Manchester United.
“Everyone at the club sends sincere condolences to Tommy’s loved ones.”
Scottish Football Association president Rod Petrie said on the organisation’s website: “Football has lost a tremendous personality in Tommy Docherty. He was tenacious on the park and a great leader off it.
“Tommy was a regular in the Scotland side in the 1950s that qualified for two World Cups, and his record as Scotland manager was impressive, albeit cut short by his decision to take the Manchester United job.
“He was on record as saying that the biggest regret of his career was leaving his Scotland managerial role and looking at the results and performances he inspired, it is hard not to wonder what might have been had he remained.
“His charisma and love for the game shone even after he stopped managing and it was entirely fitting that Tommy should be inducted into the Scottish Football Hall of Fame for his lifelong service. Our thoughts are with his family and friends at this difficult time.”
Docherty began his playing career at Celtic, before spells with Preston, Arsenal and Chelsea, and the Hoops tweeted: “We are saddened to hear of the death of Tommy Docherty who spent two years with Celtic in the 1940s. Sincere condolences go out to his family and friends. RIP.”
Chelsea also paid tribute to their former player and manager.
A club statement on Twitter read: “Tommy was a legend of our game and our thoughts are with his family and close friends at this time.”