After his often impressive yet error-strewn return to F1 this year, the 26-year-old Frenchman admitted he genuinely feared for his race seat.
"I am happy and relieved," Grosjean told France's RMC Sport.
"It has been some long and not necessarily very pleasant weeks."
In the wake of his Monza ban, Grosjean began to put his season back together but then ended 2012 badly in Austin and Brazil.
"The last two races of the season did not help the negotiations," he admitted.
"We sat down together to understand, analyse and especially consider whether we go on again.
"I was clearly concerned about going, losing what I love. When the decision came, I was very relieved," said Grosjean.
There was speculation Grosjean's turbulent season had also endangered the backing of his sponsor Total, but the French company said on Tuesday that it continues to support the Swiss-born racer.
"This is a new step in the relationship of trust that we have built together from his first laps, 7 years ago," said senior vice president Jacques-Emmanuel Saulnier.
Grosjean, meanwhile, denied Lotus decided to give him another chance for 2013 after beating the likes of reigning world champion Sebastian Vettel at last weekend's Race of Champions.
Asked when the new deal was done, he told Sky Sports: "It was just before the Race of Champions, so it was good to get there and have a weekend of fun with some good guys and really enjoy it."