The 33-year-old, who arrived at the Ligue 1 side from Barcelona last month, is one of a number of new players to join the newly-promoted side this summer.
"I'm very happy. I'm ready and full of desire and I will try to show that on the pitch," Abidal told FIFA.com.
"At 33, I must take on my role and I'm ready to do so. I spoke to the coach. I like to give, without necessarily receiving. If the others are happy, if we win, then I will be very happy."
Monaco have spent in the region of £124m on new players this summer.