The 58-year-old, originally from Belfast, was found dead in a hotel room on the Costa del Sol in the early hours of Sunday.
Spanish authorities said there were no signs of foul play but police will await the results of a post-mortem examination before deciding if an investigation is needed.
Sir Bob said Moore's work had been a huge influence on later rock acts, particularly bands such as Guns N' Roses, adding that he was also a fine blues guitarist.
"He is one of the great blues players," he told Radio 5 Live.
" Axl Rose will say that without Thin Lizzy, you don't get Guns N' Roses and that whole idea of rock and roll and Gary was sort of fundamental in developing that twin-guitar, lyrical thing like on Parisian Walkway.
"But really you didn't have to cut the skin hard to find just a great great blues player, and absolutely one of the best," said Geldof, who had been a close friend of Thin Lizzy's singer Phil Lynott who died in 1986.
Former colleagues of Moore were stunned by his death.
Founding member of Lizzy, Brian Downey, said: "I am in total shock.
"He will always be in my thoughts and prayers and I just can't believe he is gone."