The victim's name was announced by the Ministry of Defence pending formal police identification.
"An extremely popular and witty soldier, Drummer Rigby was a larger than life personality within the Corps of Drums and was well known, liked and respected across the Second Fusiliers," the MoD statement said.
Commanding officer Lt Col Jim Taylor said of Drummer Rigby: "An experienced and talented side drummer and machine gunner, he was a true warrior and served with distinction in Afghanistan, Germany and Cyprus."
Capt Alan Williamson said: "Drummer Rigby or 'Riggers' as he was known within the platoon was a cheeky and humorous man, always there with a joke to brighten the mood."