Murray masterminded the Super League side’s last Challenge Cup victory, when they beat London Broncos by a record 52-16 at the old Wembley in May, 1999.
The previous year Rhinos finished second to Wigan Warriors in the Super League table and were beaten by the same opponents in the inaugural Grand Final.
Gary Hetherington, who appointed Murray as Leeds coach after he led Hunter Mariners to the World Club Championship final in 1997, described news of his death as “devastating”.
The Leeds chief added: “He will be fondly remembered by all our fans, players and staff who knew him from his time with us.
“He was very popular and so professional in everything he did. He was an outstanding coach and mentor and he knew about all aspects of rugby league.
“The game has lost a great servant and personality and our thoughts are with his wife Amanda and his daughter Kara.”
Born in Sydney, Murray played as a scrum-half for Parramatta and South Sydney before beginning his coaching career in charge of the reserves at Penrith and then Balmain.
He was head coach of Illawarra Steelers from 1991-1995, but was sacked for siding with Super League in the dispute which split the Australian game in two.
After his two years at Leeds Murray returned to Australia, where he coached both Sydney City Roosters and North Queensland Cowboys to Grand Final appearances.
He suffered a heart attack in March and was admitted to hospital in Brisbane following a second cardiac arrest earlier this month.
The decision was taken to switch off his life support machine yesterday morning and he died several hours later.
Leeds will wear black armbands in Murray’s memory when they play London Broncos at Twickenham Stoop on Thursday.
Castleford Tigers’ coach Daryl Powell was a member of Leeds’ 1999 Wembley team.
Powell said: “I am gutted that such a great man has passed away. I thought he was incredible as a coach and as a man as well.
“Wherever he went you could see players enjoyed his personality and the way he dealt with things, not just about the game, but about life.”