Pierre Gadonneix, EDF chairman and chief executive, said the purchase of British Energy and investment in Britain's nuclear future would help EDF to stick to its commitment of reducing carbon emissions by 2020.
He said: "This investment will help to secure less volatile energy prices for our customers for the long term."
The French utility, which already supplies gas and electricity to more than five million customers in the UK, said it was committed to maintaining British Energy's headquarters in East Kilbride in Lanarkshire.
It said that British Energy's 6,000-strong workforce staff would benefit from the takeover.
Unions welcomed the announcement and the prospect of new jobs being created.
Prospect national secretary Anne Douglas said: "We know EDF and have worked with them constructively elsewhere in the UK.
"What we have to ensure now is that they understand that it is the staff that bring value to the company, more than any of the sites or grid connection points."
British Energy said that its largest shareholder - Invesco - which had played an instrumental part in scuppering a deal at the beginning of August, had agreed to accept the sweetened offer.
The deal still needs to be approved formally by British Energy's shareholders and the relevant competition authorities, but the government, which owns a 36% stake in the firm, gave its support.
It signals a major step forward for its plans to revive the nuclear industry and reduce the UK's dependence on oil and coal for its energy needs.
About 25 years ago, the supply of energy was organised along state lines, but now the industry is dominated by firms that operate across borders
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