The Japanese has secured an F1 comeback for 2014, as team-mate to rookie Marcus Ericsson.
Having failed to find a drive last year, he competed for Ferrari in the World Endurance Championship as well as taking part in F1 demonstration events.
Speaking at Caterham's Leafield headquarters on Tuesday, Kobayashi revealed that he had been offered another Ferrari contract for sportscars - as well as an expanded role on the F1 team that included simulator work.
But despite the security of such an offer, he was so keen to get back to grand prix racing that he did everything he could to persuade Caterham owner Tony Fernandes to take him when they first met in December last year.
"I am 27, I still need more to race in F1," said the former Toyota and Sauber driver. "That is why I chose to come back to F1.
"Ferrari offered me another contract, and Stefano [Domenicali] is not happy I didn't take it. But it is only my decision to be here.
"I took a risk in my life but it is important for me.
"Caterham needs some different energy and my experience is quite useful for this team. We'll see what I can do. I am quite confident."
With Caterham making no secret of the fact that it required drivers to bring financial support, Kobayashi has helped deliver a package that includes £1 million worth of funding that was raised when he asked fans to help him at the end of 2012.
Beyond that, Kobayashi also wanted to emphasise to Fernandes how eager he was by making no pay demands at all.
"I'm driving for free, it is my decision," he said. "It is just my approach. I want to do this job. This appeals to Tony, this was the message to Tony and he is happy about that.
"I want to help the team. I don't care about the money. I want to be successful in my life and I want to bring the team back successfully in my goals."
- Sports & Recreation
- Tony Fernandes