E.ON is also considering a direct acquisition in the US as well as using Powergen's North American interests as an entry point.
E.ON says it will pay shareholders 765p a share, a mark-up from the shares' Friday closing price of 706p.
But the takeover must first by scrutinised by a host of regulators with the deal not expected to be finalised until Spring next year.
The European Commission, UK energy watchdog Ofgem, several US state utility regulators and the US Federal Energy Regulatory Commission must all clear the deal before it gets the green light.
Aggressive expansions
E.ON, based in Dusseldorf, was formed last year from the merger of German utilities Veba and Viag.
It is known to have aggressive expansion plans, and previously indicated that it considered Spain and the UK as the most attractive European markets for acquisitions.
E.ON is also considering a direct acquisition in the US as well as using Powergen's North American interests as an entry point.
"We are now getting ready for a double jump across the Channel and from there on across the Atlantic Ocean," said E.ON Chairman Ulrich Hartmann.
The company is seeking investments outside Germany, where tough competition has eroded earnings at its core energy business.
Powergen has a well known brand name in the UK, following its high profile advertising campaign which includes sponsoring weather reports.
It will remain a subsidiary of E.ON, retaining the Powergen brand, and job losses are not expected.
Market shake-up
The UK's liberalised electricity market is proving popular with foreign investors.
Press reports on Sunday said that Electricite de France (EdF) was preparing a £1.5bn bid for electricity distributor Seeboard.
Seeboard has penetrated the gas and electricity market in the southeast of England, but was recently put up for sale by its US owner, American Electric Power.
EdF already owns the majority stake in London electricity alongside Virgin Energy.
Rising shares
By early afternoon, Powergen's shares rose by 11p to 717p on the back of the news which the markets had largely already factored in.
Powergen stock has only closed above the offer price of 765p once in the last two years, peaking at 769p for one day in May 1999.
E.ON stocks soared despite early fears that the firm may have offered to pay too much.
The additional news that E.ON is to streamline its business and focus exclusively on energy caused its share price to soar 6.28% to 55 euros at 1425 GMT.