The 25-year-old has previous F1 experience, having tested with HRT for two days in Abu Dhabi in 2011.
Christijan Albers, who was appointed as Caterham's new CEO following a management takeover at the start of July, said Berthon fitted perfectly with the programme's aim of helping drivers to prepare for F1 by embedding them in the team's on- and off-track operations.
"We are very pleased to welcome Nathanael into our Development Driver Program," Albers said.
"He is an exciting young talent with a proven track record in the feeder series for F1 and as he already has F1 experience he fits very neatly into our team. We will work closely with him to help him reach his full potential and are all excited about seeing him continue to grow as a driver, in and out of the cockpit."
Caterham have already run Robin Frijns and Alexander Rossi, both 22, in Formula One practice sessions during the 2014 season. Will Stevens, meanwhile, is another of their juniors, and is driving for the team during the two-day in-season test at Silverstone, alongside GP2 drivers Julian Leal and Rio Haryanto.