He doesn't want you to write the letter for him, just to remind him about your major contributions to the project. I'd write it like a resume, with bullet points for your main accomplishments. If there is some interesting story that you'd like him to use, by all means write a bit more about it so he'll be familiar with the details.
I'd also shy away from using the 3rd person, but that's just me.
Finally, if there is some personal quality you feel that he needs to stress for some reason, mention it. If you don't have a compelling reason though, just trust that he will do the right thing for you.
And of course be grateful that he is so keen to write you a good letter!