But he struggled to hold down a regular place in Arsene Wenger's side last season because of the emergence of Mathieu Flamini and the impact of Cesc Fabregas.
He also lost the club captaincy to William Gallas.
Gilberto was keen to join up with Panathinaikos boss Henk ten Cate, who left his post as Chelsea assistant coach at the end of last season.
"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."
The 31-year-old has followed AC Milan signing Flamini and Barcelona recruit Alexander Hleb out of the Emirates.
The exodus means Wenger will now look to summer signing Samri Nasri and Abou Diaby to cement their places in midfield with �5m signing Wales teenager Aaron Ramsey a prospect for the future.
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