The Belfast-born guitarist was 58.
Thin Lizzy manager Adam Parsons told the BBC that he was found early on Sunday.
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.
Bell said on Sunday that he was still "in shock" at Moore's death while on holiday in the Costa del Sol.
"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."
A message on Moore's official website says,"It is with deep sorrow and regret, that we have to announce that Gary Moore passed away while on holiday in Spain last night." (ANI)