The three sites identified for clearance include a notorious dump in Bickershaw, near Wigan, which caught fire last summer, forcing schools nearby to close.
Residents living in the area have previously told the BBC they feel “forgotten about” as they are surrounded by rats, flies and an “unbearable smell”.
Nicha Rowson, a beautician who has been forced to move her studio out of her home because of the stench, said the decision to clear up the site was “amazing news”.
“I’m sure the community that I’ve been campaigning for is just as happy as I am with the news,” she added.
However, she said it should not have taken so long for a decision to have been made, saying: “Money’s been put before residents’ physical and mental health.”
She added that it “was not good enough” that the culprit had not yet been prosecuted and the taxpayer had now been left to pay for the clear-up.
The other two sites earmarked for clearance are a 20,000-tonne dump on an industrial site in Sheffield and a 10,000-tonne tip in Hyndburn, Lancashire.
The government, which has not yet said how much the clear-ups will cost, still has to carry out site-specific assessments to ensure the logistics of any clearance are feasible before they can start.
Earlier this year, the BBC revealed that among hundreds of illegal dumps operating across England, at least 11 are so-called “supersites”, containing more than 20,000 tonnes.
Tens of thousands of tonnes of waste has been dumped on the land in Over, near Gloucester, and witnesses have told the BBC that, at its height, 30-50 vehicles were going onto the site to dump rubbish every day.