In Goofy's Hysterical History Tour, the player takes command of Goofy himself who gets his dream job as janitor at The Ludwig von Drake History Museum. However, his rival Pete is determined to get him fired and sabotages the exhibits and scatters pieces throughout various time periods. Armed with a new gadget, the Extend-O-Hand, Goofy must travel to the past and recover the pieces before the morning.

The game is a platformer, where Goofy must travel through various stages ranging from Prehistoric times, Medieval times, Colonial America and the Wild West among many others, collecting items and power-ups and defeating Pete's henchmen using the Extend-O-Hand. After collecting all the pieces, Goofy then must face Pete himself.

On the even of the big opening of four brand new exhibits at the Ludwig Von Drake History Museum, Professor Von Drake wants everything to be just right. So he's decided to have a heart-to-heart talk with one of his janitors--Goofy!

The professor tells Goofy that this is his last chance to prove himself. Goofy's blundering has been slowing down the general upkeep of the museum. The other janitor--that nasty old Pete, Goofy's longtime arch-rival--has been letting the professor know about all the slip-ups Goofy's been making. If anything goes wrong with the debut of those exhibits tomorrow because of Goofy's goofiness, the professor will have no choice but to fire him!

But Goofy knows that he can do the job. His new invention, the Extend-O-Hand, has tons of attachments designed to make his custodial duties easier to perform. The professor is impressed with the Extend-O-Hand and Goofy's initiative, and tells him that if he and his new tool can get the job done tonight, he'll not only get to keep his job, but he'll be promoted to head Janitor!

Nothing could make Pete angrier than that! He's been hiding nearby and eavesdropping on this entire conversation! How could a klutz like Goofy deserve anything, even with that stupid Extend-O-Thingy?!