The bomb squad was called in after the items were checked during a stock assessment in Dorking museum in Surrey. The Army has now blown them up, the Daily Mail reported.
Kathy Atherton, from the museum, said staff would investigate how they got there but suspected they were historic donations from souvenir collectors.
They were discovered by volunteers two months before the end of the museum's three-year refurbishment programme.
"A volunteer took photos and sent them off to the Imperial War Museum, and they came back, identified them and said 'you can't be sure with these things, even if they're old they may still be explosive, you really need to get some advice on this'," she said.
"At that point we contacted the police who got the bomb squad in from Aldershot," she said.
"They've probably been in the museum's collection for years, we've been collecting since the 1950s," Atherton added.
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"There's a whole generation of people who during the war went and collected souvenir items, someone's probably had it in the back of a wardrobe for years and at some point deposited in the museum and they've been in our stores ever since," she was quoted as saying by the paper.
The Ministry of Defence said the Royal Logistic Corps removed and destroyed a two-inch illumination mortar round and 20 mm cannon shell.
They were on show alongside a 1940s war map showing where planes crashed, parachute landings took place and bombs, rockets and incendiaries fell on the Dorking area.