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 French Grand Prix will return to the Formula 1 calendar after an absence of 10 years, the sport's boss Bernie Ecclestone has said.