Probably not very easily
Of all the times the Imperius Curse was cast in canon, the only time it seems to have been broken by magic was during Harry, Hermione and Ron's Gringotts break-in. This was done by the Thief's Downfall, a waterfall that removes enchantment.
“The Thief’s Downfall!” said Griphook, clambering to his feet and
looking back the deluge onto the tracks, which, Harry knew now, had
been more than water. “It washes away all enchantment, all magical
concealment! They know there are imposers in Gringotts, they have set
off defenses against us!”
—Harry Potter and the Deathly Hallows
However, it is highly unlikely that such magic is widely available. First, Voldemort could not have Imperiused so many Ministry employees if such protections were in place. Second, the animosity between wizards and goblins is very high, with wizards often denying goblins rights, and goblins in turn keeping their magic secret. It seems likely that the the Thief's Downfall was an enchantment known only to the goblins, and of which witches and wizards generally had no knowledge (indeed, since goblins have a different brand of magic, perhaps wizards could not reproduce it).
We also know that the Imperius Curse can be broken through one's own strength of will, as Harry did, for example.
In all other cases, the Imperius Curse seems either to have worn off, or to have ended with the death of its caster, or been lifted voluntarily. It is also possible that severe mental or magical trauma can life the curse. For example, the Unspeakable Bode was placed under the Imperius Curse in Order of the Phoenix, but was later killed by Death Eaters to keep him silent, indicating that the curse was no longer active (clearly, it was not removed, since it was not even noticed). It might have worn off, or been broken by the mental damage caused by the spells on the prophecy. Something similar is certainly possible with Memory Charms, which can be broken by torture.
Needless to say, extensive torture is probably not considered an acceptable method of keeping the Ministry Imperius-free.
There is no evidence that safe, widely available magic can reverse the effects of the curse.