British Energy owns eight of the UK's 10 operational nuclear power plants, and a takeover would potentially hand its new owner a monopoly on the construction of a new generation of facilities.
EdF last month pulled out of a planned £12bn takeover of the nuclear generator after unexpected shareholder opposition.
The French generator has now made an approved offer of 774p, up 9p per share on the original proposal, and this has been accepted by the British Energy board.
"We are delighted that the British Energy board has unanimously accepted this offer," said EDF chairman Pierre Gadonneix.
"This paves the way for investment in the UK."