The former Chelsea midfielder was a free agent after his contract with AC Milan expired at the end of the 2014-15 season.
The 32-year-old will now spend the next two years in Athens, where he will look to help Panathinaikos end a five-year wait for a league title.
"I am very happy to be here and I'm very much looking forward to starting my new career with Panathinaikos," Essien told reporters.
"I am a winner and I have come to Greece to win more trophies and to do whatever I can for my new team.
"I did not expect such a reception. When I saw the fans, it was a great pleasure for me to see that they came out to greet me. It was incredible. I want to thank them and I will do everything I can to repay them."
Panathinaikos will enter next season's Champions League in the third qualifying round, having finished second in the Greek table last season.