The arrival of Kobayashi has marked the Japanese driver's return to F1 after a season with Ferrari's GT programme in the World Endurance Championship.
"It's a great feeling to be back as an F1 race driver and I'm really pleased it's with Caterham," Autosport quotes Kobayashi as saying.
"Throughout all our discussions I've been very impressed with where they want to take the team, and how much investment has been made already to help them achieve their goals."
Ericsson, 23, has been promoted to F1 following four years in GP2, which resulted in a sixth-place finish in last season's standings.
"This is a very proud day for me and everyone has helped make my F1 dream come true," said Ericsson.
"I'll be making the step up to F1 with Caterham in 2014 and I'm already excited about the season ahead, and the first race in Australia in particular."
Both drivers have experience in F1, with Kobayashi previously driving for Sauber for two years, while Ericsson drove for the Brawn team in the rookie tests in 2009.