The board of state-owned electricity utility EDF approved a compensation package worth at least €400 million ($430 million) for the shutdown of the Fessenheim nuclear plant, a source close to the matter said.
EDF, which is 85.6 percent owned by the state, agreed the plan with the French government last August.
The closure of the twin-reactor plant is part of a plan to dramatically reduce the country's dependence on atomic energy.
The plant in Fessenheim on the border with Germany about 100 kilometres (60 miles) south of Strasbourg has been in operation since 1977.
Fessenheim, located on a seismic fault line, has worried French, German and Swiss environmentalists for years.
Last year Germany demanded that France close down Fassenheim following reports that a 2014 incident there was worse than earlier portrayed.
"This power plant is very old, too old to still be in operation," said a spokeswoman for Germany's Environment and Nuclear Safety Minister at the time.
"That's why the environment minister demands its closure at the earliest possible date," he said, reiterating Berlin's earlier demands.
France's Nuclear Safety Agency said that safety at the plant was ”overall satisfactory”.
Hollande, who leaves office in May, vowed during campaigning in the 2012 election to close the facility, as part of a promise to reduce the share of nuclear in France's energy mix from 75 percent to 50 percent and increase the share of renewables.
But the plan ran into stiff opposition from the conservative opposition, which sees France's nuclear park as a guarantor of the country's energy independence and a source of cheap electricity.
Ministers insisted Fessenheim would close last year, but little happened despite lots of talk.
Fessenheim is not the only French plant that has unsettled its European neighbours.
Luxembourg and Germany have also raised concerns over another power plant, at Cattenom, and the duchy has forwarded to the European Commission a study commissioned by Germany's Greens party, which according to Luxembourg "listed the plant's security problems".
Meanwhile, the Swiss canton of Geneva has filed a complaint against French nuclear plant Bugey located in the neighbouring French region of Ain, claiming that it "deliberately puts in danger the life of others and pollutes the waters".