The long-awaited announcement completes the 22-man grid for the season starting in Australia in March and marks a fresh start for the Malaysian-owned team who have yet to score a point in four years.
The two replace Frenchman Charles Pic and Dutch driver Giedo van der Garde.
"I'm delighted that we've been able to bring Kamui back. He is a very popular driver and it's very good for the whole team we've been able to attract such an exciting driver to join us at a critical point in our development," said Caterham principal Cyril Abiteboul.
"His pace speaks for itself, and his extensive experience of developing cars, particularly in his years with Toyota, will be incredibly important for us as we tackle one of the most challenging seasons F1 has ever embarked upon."
Kobayashi, who set up a website to raise the funds needed to secure a Formula One return after losing his Sauber seat in 2012, competed for Ferrari in sportscars last year.
He said it was a great feeling to be back and thanked all those fans who had contributed to make it possible.
"Their donations and gestures gave me extra strength to come back fighting and I am very pleased that the money they raised not only helped me but will now go to helping Caterham progress this year," he said.
"Every single one of you who helped with 'KAMUI SUPPORT' will race with me in 2014 and that makes me very proud."
The Japanese finished third in his home race at Suzuka in 2012 and will be his country's sole representative on the starting grid.
Ericsson, 23, will be making his debut after competing in the junior GP2 series last year and becomes Sweden's first Formula One race driver since Stefan Johansson in 1991.
"It's obviously great for Sweden that we'll have a Swedish driver back on the grid in 2014," he said.
"This is what I've been working for since I first started racing karts back when I was nine years old, and now I know I'm ready for the step up to F1.
"Caterham is a young team and together we can take on the challenges the new rules will present in 2014."
Formula One has a new turbocharged V6 engine, replacing the old V8s, as well as other major technical changes to come to grips with this season.
Ericsson will not be the only rookie from Scandinavia, with Denmark's Kevin Magnussen making his debut at McLaren.
Caterham said American Alexander Rossi would remain the reserve driver at weekends when he was not competing in GP2 with Dutchman Robin Frijns otherwise filling the role and having some time in the car during the year.
(Reporting by Alan Baldwin, editing by Patrick Johnston)
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