The team said in a statement at the U.S. Grand Prix on Friday that the 24-year-old, who won the GP2 support series last year, would join Venezuelan Pastor Maldonado in their 2016 lineup.
"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," said chairman Gerard Lopez.
No details about the length of the contract were given by either party.
Palmer has been Lotus reserve this season, taking part in practice sessions. He replaces Frenchman Romain Grosjean who is joining the U.S.-based and Ferrari-powered Haas F1 team who are due to debut next year.
The timing of the announcement came as a surprise, with the financially-struggling team in the throes of being taken over by Renault, who previously owned them before becoming only an engine supplier.
Palmer and team officials said Renault had been involved in the decision.
Jonathan Palmer started 83 races for Williams, RAM, Zakspeed and Tyrrell between 1983 and 1989 with a highest placing of fourth in Australia in 1987.
"Jolyon's definitely better than me," the proud father told reporters as he sheltered under an umbrella in the rainswept paddock.
"He's a lot less intense than I was and more relaxed and a better overtaker. He's a better racer. It just comes to him a lot more naturally than it did to me.
"I was obviously pretty good but I think I got there through tenacity and being pretty clever on setups and things but in terms of raw driving ability, Jolyon is well above me," he added.
Jolyon said he had wanted to be a grand prix driver from about the age of three, even if he only started karting at the comparatively late age of 13.
His deal means Britain has three confirmed drivers for next season, with world champions Jenson Button and Lewis Hamilton at McLaren and Mercedes, and Will Stevens hoping to stay at Marussia and make it four.
It also leaves McLaren reject Kevin Magnussen, and Belgium's 2015 GP2 champion Stoffel Vandoorne, with little chance of securing a race seat for next year.
"I'm hoping the car's going to be strong and I can show what I can do really," said Palmer, who will take part in all the remaining practice sessions of the season. "Now I'm in Formula One, I want to be fighting at the sharp end."
(Reporting by Alan Baldwin, editing by Tony Jimenez/Ian Ransom)
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