The 23-year-old American made his GP2 debut with the squad at Monza last year and also competed at Marina Bay, taking a best finish of 15th.
He is optimistic of becoming a regular points scorer alongside his new team-mate Rio Haryanto.
"I am excited to be joining Addax for the 2013 GP2 season and wish to thank all involved for making this possible," Rosenzweig said.
"Having raced in the final two rounds of the 2012 championship with Addax, I know what an opportunity this represents to be working with them again.
"The race calendar has some great circuits and I am looking forward to hitting the ground running. I will do my best to score as many points as possible over the course of the season."
Rosenzweig's full-time programmes during the past two years have come in Formula Renault 3.5. He finished 15th in the 2011 points and set one fastest lap, and added 21st overall last year. He has also been a podium finisher in the F3 Euro Series.
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