The 31-year-old passed a medical and signed a three-year deal after Arsenal accepted an offer of around £1m.
"I came to Greece because I have big ambitions, it's very important for me to be able to continue to give my best. I couldn't say no to the offer."
"I'm sure we will qualify through to the group stages of the Champions League," added Gilberto. "I'm exited about being a Panathinaikos player."