The Briton has served as their reserve driver this year, contesting 10 practice sessions in total so far, after clinching the 2014 GP2 crown. He will compete alongside Pastor Maldonado next year, replacing Haas-bound Romain Grosjean.
"It feels pretty unbelievable!," Palmer said. "It's been such a long journey and I'm so glad to have been confirmed as a race driver with the team next year.
"A lot of hard work has gone into preparing for this to happen and into proving what I'm capable of delivering. I'm very grateful to everyone who has so far helped me at the team; I'm now looking forward to 2016 and to build on the experience that I already have.
"Getting into Formula 1 has never been harder. When I won GP2 in 2014 I felt that I was ready to move up back then so it feels like it has been a long time coming. At the same time, this year has been very good. I have enjoyed working with the team and ultimately it has given me the chance to prove what I'm capable of. I'm absolutely ready for it now!"
Palmer said his duties as reserve driver had "opened my eyes to the world of Formula 1," and also helped him to prove his credentials.
"I have learnt a huge amount with the team this year," he added. "GP2 is high level, the drivers are good and the car is very solid but F1 is another level. The technology involved is immense and so advanced, there is a lot to get your head around. I'm now better prepared than ever.
"To be getting a lot of mileage in the car was the most important aspect for me this year. It has also proved valuable to show everyone in the team what I can deliver behind the wheel.
"I'm very pleased to be working with Pastor next season. We have worked well together this year and I've been driving alongside him in FP1 already. It's good to know that there will be continuity."
Team principal Gerard Lopez added: "We are very pleased to announce that exciting British racing talent Jolyon Palmer is promoted to a race seat with the team for next season.
"We've seen Jolyon's hard work and talent this season in the way he's approached his third driver role and he is a really popular choice for the team.
"As well as having a great future ahead of him behind the wheel, Jolyon is an intelligent and highly marketable asset to the team. He deserves this opportunity, and everyone at Enstone is excited to see what he can achieve next year."