A Hibs statement said Reilly, who was part of the club's 'Famous Five' forward line in the 1940s and 50s, died peacefully in hospital.
Reilly scored 238 goals during his 12-year career at Easter Road, helping the club win three Scottish league titles.
He was also part of the Hibs side which in 1955 became the first from Britain to compete in the European Cup.
Reilly also scored 22 goals in 38 appearances for Scotland, among them five in five games against England at Wembley.
Hibs chairman Rod Petrie said: "We all feel the loss of a true Hibernian great, but our hearts must go out first to Lawrie's widow Iris and to his family. Our thoughts are with them at this sad time.
"The term legend gets bandied about, perhaps too easily, but Lawrie was a genuine legend.
"He grew up as a Hibernian fan and he spent his entire career with the club he loved. He was undoubtedly one of the club's greatest ever players, revered by all who loved attacking and entertaining football. He was also one of Scotland's greatest ever strikers.
"Lawrie retained his lifelong passion for the club he graced as a player and was a regular attender at matches, a matchday host and was one of the club's Champions. He will be sadly missed."
Campbell Ogilvie, the SFA president, added: "Lawrie was a friend of the Scottish FA and his achievements for Scotland have endured to this day. Hibernian's Famous Five are part of football folklore and Lawrie retained a love for football throughout his life.
"He was a gentleman first and foremost but he was a truly fantastic footballer and terrific ambassador for the game."
"Lawrie remains Hibernian's most capped player of all time and was inducted into the Scottish Football Hall of Fame in 2005."
Reilly was the last survivor of the Famous Five, one of the most feared frontlines of its generation, which also included Willie Ormond, Gordon Smith, Bobby Johnstone and Eddie Turnbull.