French media reported that a five-year deal had been agreed to host the race at Le Castellet, near Marseille.
Ecclestone told Reuters: "Yes, I think it will happen," adding that it would be held in late July, not a month later as the initial reports had suggested.
France hosted the first ever grand prix in 1906 but lost its slot in 2008.
There have been several attempts since to revive the race but this one looks to be the first to succeed.
A news conference has been organised for an announcement about the future of the French Grand Prix in Paris on Monday, to be hosted by Christian Estrosi, the president of the Regional Council of Provence-Alpes-Cote d'Azur.
The French sports newspaper L'Equipe reported that a five-year deal had been agreed with the Provence-Alpes-Cote d'Azur region in association with the city of Toulon, department of Var and the French motorsport association.
Le Castellet - also known as the Circuit Paul Ricard - last hosted the French Grand Prix in 1990. From 1991-2008 it was held at Magny-Cours in central France.
Ecclestone's family trust owns the track but the 86-year-old said: "It's nothing to do with them at all. I think they are renting it to the people that are going to be the promoters."
He said the race would be held on "more or less sort of the German date probably", without specifying what that meant for the future of the German Grand Prix.
That race has dropped off the calendar for next year because the Nurburgring, one of two venues that alternate as hosts, cannot meet its financial obligations under its contract with F1.
But Hockenheim, which held the race in 2016, has a contract to do so again in 2018.
The return of France will be greeted with widespread delight by both F1 insiders and fans of the sport.
This is because of its historic significance and because it is another race in the sport's heartland of Europe rather than, as has been the recent trend for new events, in a country where the sport has limited support and no heritage.
F1 is in the process of being bought by US group Liberty Media, and it has said that protecting races in F1's heartland is a major priority, along with expanding its presence in the US, the rest of the Americas and Asia.

The budget was passed with a majority of only eight votes - 153 to 145.
"This budget is a difficult task for a government that wants to leave its mark with social justice," Prime Minister Alexis Tsipras told lawmakers.
He agreed to a batch of economic reforms in August to secure a euro zone bailout of up to €86bn ($93bn; £62bn).
His leftist-led government has been under pressure to deliver tangible benefits to its poorest citizens since the agreement.
The budget makes €5.7bn in public spending cuts including €1.8bn from pensions and €500m from defence. It also includes tax increases of just over €2bn.
Despite the cuts, the budget will still have a greater deficit than the 2015 budget.
Earlier this year Greece reluctantly agreed to the strict conditions of its third international bailout in five years.
After losing his majority in August as a result, Mr Tsipras called an election and was returned to power in September with 35% of the vote.
Representatives of the euro zone, the European Central Bank and the International Monetary Fund return to Greece on Monday for more talks about pending reforms of the pension and tax systems and public administration.
The euro zone has also held out to Greece the possibility of long-term debt relief after a review of progress under the new bailout.
However, it has said that relief would come in the form of longer delays before repayments start or finish, not a reduction - or so-called "haircut" - in the amount that has to be repaid.
The French Grand Prix will return to the Formula 1 calendar after an absence of 10 years, the sport's boss Bernie Ecclestone has said.
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Greece's parliament has narrowly approved the 2016 budget that includes sharp spending cuts and some tax increases amid economic recession.