Edinburgh fell ill five days ago after reportedly returning from Spain, where he had been to watch the Champions League final.
“We are completely heartbroken by this tragedy,” said the Orient chairman Nigel Travis. “All our thoughts and love are with the Edinburgh family and we know from the messages that have flooded into the club over the last week that the wider football world will share our sentiments.
“The success that Justin brought to Leyton Orient was incredible, but more importantly the impact he had on us all as a winner and a wonderful, inspirational human being will be his legacy and will stay with us forever.”
Leyton Orient FC also posted an official statement on Twitter which read: “It is with profound and utmost sadness that Leyton Orient announces its manager Justin Edinburgh has passed away.”
Edinburgh had travelled to Madrid last weekend to watch Tottenham Hotspurs play Liverpool.
He played for Spurs for a decade, making 215 Premier League performances for his beloved team.
Spurs also paid tribute to the footballing legend, adding: “We are deeply saddened and shocked to hear of the passing of Justin Edinburgh.
“Our heartfelt condolences and thoughts go out to his family and friends at this terribly difficult time as well as everyone that worked alongside Justin at Leyton Orient.”
Edinburgh took over Leyton Orient in 2017, and led them to promotion to the Football League back in April.
He started his football career as a left back for Southend United before moving to Spurs in 1990, where he remained until 2000 when he was sold to Portsmouth for £175,000.