Edinburgh, the former Tottenham Hotspur defender, joined English League Two side Orient as coach in 2017 and led the club back into the Football League as National League champions in 2018-19.
"We are completely heartbroken by this tragedy," Orient chairman Nigel Travis told the club's website.
"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."
Edinburgh started his playing career at Southend United before he moved to Tottenham in 1990.
He made 215 appearances for Spurs, helping them win the FA Cup and League Cup during a decade at White Hart Lane.
(Reporting by Peter Hall, editing by Ed Osmond)
