As part of the transaction, E.ON and EQT will form a joint venture, which will own 100 percent of Energy from Waste, Germany's leading waste incineration business.
EQT will own a 51-percent stake in the business, while E.ON holds the remaining share.
"Together with our partner, we want to guide E.ON Energy from Waste to a successful future as an independent company," E.ON chief executive JohannesTeyssen said in a statement.
E.ON said that the transaction is expected to close in the first quarter of 2013, subject to anti-trust approval.
Like other energy firms in Germany, E.ON has been hit hard by Berlin's decision to phase out nuclear power in the wake of the disaster in Fukushima, Japan.
E.ON said last month it would no longer achieve its sales targets next year and booked a net loss in the third quarter. It has launched a major debt-reduction drive.
With the joint venture, E.ON said it had achieved more than €14 billion of its target to generate €15 billion from the sale of assets by the end of 2013.
EQT is one of Sweden's leading private equity groups, consisting of 14 funds with nearly €19 billion in capital.
Since its launch in 1995, EQT has invested more than €11 billion in around 100 companies.