The Edinburgh-born centre-forward was a member of the Easter Road club's 'Famous Five' forward line alongside Gordon Smith, Bobby Johnstone, Eddie Turnbull and Willie Ormond and helped the side win three league titles in the late 1940s and early 1950s.
He was capped 38 times for Scotland and scored five goals against England - more than any other Dark Blues player.
Strachan, who grew up a Hibs supporters, took time out of his preparations for next month's meeting with the Auld Enemy at Wembley to pay tributes to a man idolised by the Leith club's faithful.
He said: "I used to see Lawrie regularly when I went to Easter Road. He was a big hero of my father and it's not great news. But he has left us with some fantastic memories.
"He scored five times [against England] but, even though I met him so many times, he never mentioned that. It's a measure of how much a gentleman he was that he never mentioned that.
"Great players never tell you what they did - people already know. And he was a great player, that's for sure."
In a statement released by Hibs, club chairman Rod Petrie paid tribute to Reilly, who netted a record 187 league goals for the club.
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."
Reilly's passing comes just days after former Rangers manager Davie White died, aged 80, and Strachan - who played under him at Dundee - added: "It's been a double blow this week.
"Davie was somebody who looked after me really well when I was a kid at Dens. Partly because of him I am where I am today."