Ocon, 20, is contracted long-term to Mercedes, Force India's engine provider, and has been racing for Manor in the second half of this season.
He replaces German Nico Hulkenberg, 29, who has moved to Renault, and will be alongside Mexican Sergio Perez, 26.
"Spending half a season at Manor Racing has given me some valuable experience and I feel ready for this," said Ocon.
"It's something I've been working towards my whole life and I intend to grab this opportunity with both hands.
"I want to say thank you to everybody at Manor and especially to Mercedes-Benz for their support and belief in me. I can't wait for 2017 and my first full season racing in Formula One."
Ocon joined Manor for the Belgian Grand Prix at the end of August and has impressed increasingly as the season has progressed.
Both he and Manor team-mate Pascal Wehrlein are contracted to Mercedes' junior driver programme.
Ocon's best results for Manor have been the 16th-placed finishes he secured at the Belgian Grand Prix and at last month's Malaysian Grand Prix.
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French driver Esteban Ocon will race for Force India in 2017 after agreeing a "multi-year deal", with the team.