Moore, 58, was originally from Belfast and was a former member of the legendary Irish group Thin Lizzy.
Adam Parsons, who manages Thin Lizzy, told the BBC that Mr Moore had died in the early hours of Sunday morning.
Mr Moore was originally drafted into Thin Lizzy by its singer Phil Lynott. He later gained acclaim for his solo work and was a former member of the Irish group Skid Row.
The Northern Ireland guitarist was only 16 when he moved from Belfast to Dublin in 1969, to join Skid Row, which featured Lynott as lead vocalist. He was later brought into Thin Lizzy by Lynott to replace the departing Eric Bell, another guitarist from Northern Ireland.
Mr Bell told the BBC on Sunday he was still "in shock" at Mr Moore's death.
"I still can't believe it," he said. "He was so robust, he wasn't a rock casualty, he was a healthy guy. He was a superb player and a dedicated musician."
Scott Gorham of Thin Lizzy said it been a pleasure to share a stage with Mr Moore. "Playing with Gary during the Black Rose era was a great experience, he was a great player and a great guy," he said. "I will miss him."
Niall Stokes, the editor of the Irish music magazine, Hot Press, described Mr Moore as a "genius".
The lead guitarist received critical acclaim for his work on the 1974 Thin Lizzy album, "Nightlife," but would never be constrained by the music group format. A year earlier, he had released his first solo album, "Grinding Stone," and his virtuoso playing was to make him a recognized artist in his own right.
Although returning to Thin Lizzy briefly in the late 1970s, his solo work continued to garner interest and he also enjoyed UK chart success with Lynott, via singles "Parisienne Walkways" and "Out In The Fields."
Throughout his career, Gary Moore was to embrace a range of genres including blues, metal and hard rock. He performed on stage with a range of major artists and released 20 studio albums.
Gary Moore
Gary Moore – Still Got The Blues
Live - 2008
Gary Moore – Parisienne Walkways
One Night In Dublin: A Tribute To Phil Lynott DVD