A joint statement welcomed "the conclusion of the Inter-governmental Agreement (IGA) on the acquisition of 36 Rafale fighter aircrafts in flyaway condition, except for some financial issues".
“We are very happy that we have formed an agreement for purchase of 36 Rafale aircraft with France,” Modi said at a joint press conference with Hollande, who is on the second day of a visit to India.
Hollande said the signing was a "decisive stage" in the long-drawn-out negotiations that started in 2012.
Both leaders said that the financial issue would be resolved "as soon as possible", without giving details.
A senior French official told reporters on Sunday that the two sides are still negotiating the price, which experts say could be about five billion euros.
The number of jets, announced by Modi on a visit to Paris last April, to be bought is substantially lower than the 126 first envisaged in 2012.
Neither leader referred to the possibility of Delhi buying further 18, as had been suggested by sources last week.
Dassault's share price rose three per cent on Monday morning after the announcement.
Hollande also said that there had been progress on the question of six nuclear reactors French nuclear giant Areva hopes to build in Jaitapur in Maharashtra state, although Modi made no reference to them.
Disagreements over the price have hampered negotiations recently.
French companies will invest nine billion euros in India over the next five years, chiefly in the industrial sector, French Finance Minister Michel Sapin, who was also in Delhi, said.
“Over the last five years, French companies have invested more than one billion dollars per year in India,” Sapin said in a speech to the Federation of Indian Chambers of Commerce and Industry in New Delhi. “We estimate that they will continue to invest at least 10 billion dollars over the next five years.”