Grosjean took three podium finishes on his way to eighth in the championship in 2012 with 96 points.
The 2011 GP2 champion had come under criticism for his driving style, having received a one race ban for causing an accident at the Belgian Grand Prix.
Grosjean will partner Kimi Raikkonen at the Enstone based team for a second successive season.
"It’s fantastic for me to be continuing with Lotus F1 Team for 2013," said Grosjean.
"It’s superb to have the support of everyone at Enstone. I’m really looking forward to rewarding their faith when we take to the track in Australia. I learnt a lot in my first full season in Formula 1 and my aim is to put these lessons into practice with stronger and more consistent performance on track next year."
"There are a lot of exciting developments occurring behind the scenes at Enstone and I am very excited with the prospect of the E21. I’ve already had my seat fitting and spoken with all the personnel involved with the build of the new car ; I just can’t wait to get behind the wheel."
Team principal Eric Bouiller believes that with a stable driver line-up, Lotus can improve on a strong 2012.
"Romain is a great talent and we are pleased that he is continuing with us for a second season. With the continuity of two exceptional drivers like Romain and Kimi we are well placed to build on our strong 2012 with even better results in the year ahead."
"Both drivers worked very well together in their first year as team-mates, and I think there is the potential of even better things from the season ahead. We were regular visitors to podiums in 2012 and we certainly intend to continue with this trend in 2013".