The new agreement signals an end to the 10-year pursuit of Edison by EDF, with the drawn-out talks leading to a sharp ratings downgrade of the Italian company to junk status.
The agreement, subject to regulatory and corporate approvals, would increase EDF's stake in Edison from around 50 percent currently, via direct and indirect holdings, to around 80.7 percent, EDF said in a statement.
In exchange, Italian shareholders would gain control of the electricity production unit Edipower, which will enter into an agreement with Edison to supply it with gas for half of its needs for six years, the statement added.
"This agreement will allow the emergence of two energy champions in Italy, which thanks to their stabilized organization and a relaunch of their activity will contribute to the recovery of the growth of the Italian economy," EDF said.
It said the Italian shareholders would pay €800 million ($1 billion) to acquire the stake in Edipower, which is €100 million more than it will pay to acquire the stake in Edison.
EDF's shares slid 0.62 percent to €18.31 in afternoon trade.
The new agreement follows months of difficult negotiations, with Italian shareholders threatening last week to abandon talks if they did not get control of Edipower.
Last week Fitch ratings agency cut Edison's rating by three notches to junk status, from BB- from BBB- due to "the negative impact of the prolonged negotiation process" as well as weak liquidity.
However Fitch said the rating could improve if EDF won clear control of the company.
EDF said it expected approval of the deal from the various holding companies by the end of January with final contracts to be signed by February 15th.
EDF has been involved with Edison for a decade, buying a stake in its holding company in 2001 and teaming up with carmaker Fiat to take control, only to have the Italian government limit its voting power.
In 2005 it teamed up with other Italian shareholders to jointly manage Edison, but disagreements over strategy led EDF to seek to take majority control.
Founded in 1884 and based in Milan, Edison is Italy's oldest electricity company and is currently in second place in electricity generation behind Enel, producing 41.8 terrawatt hours of electricity or 14.6 percent of the country's total in 2010.
Edison is also Italy's number two gas company, with 19.1 percent of the market last year, behind ENI.
EDF's takeover of Edison is the latest in a series of high-profile acquisitions of Italian businesses by French companies, some of which have sparked controversy and efforts by the government in Rome to block the deals.
The stealth acquisition by Lactalis of a 29 percent stake in Italian dairy company Parmalat, enough to control its operations due to a diverse shareholder base, earlier this year spurred government-supported efforts to put together an Italian-led buyout.
The Italian efforts ultimately failed and Lactalis, the company behind the President camembert cheese brand, became the world's biggest dairy company after taking control of Parmalat in June.
In the luxury sector France's LVMH, the world's top luxury retailer, snapped up Bulgari for €4.3 billion in June.
Its rival PPR, which already owned Gucci and Bottega Veneta, in November added to its stable Brioni, famous for dressing James Bond in the fictional British spy's latest film outings.
Italy's government blocked in 2008 a takeover of Alitalia by Air France-KLM, which currently holds a 25 percent stake in the troubled airline. Reports in the Italian media indicate that some Italian shareholders want to bring forward from October 2013 the date they can sell Alitalia shares to Air France-KLM.