The 39-year-old played 36 Serie A games in 2020-21 and contributed five goals and six assists in the process.
Palacio arrived from Inter on a free transfer in August 2017 and first arrived in Italy when he signed for Genoa in 2009.
“After 132 appearances and 20 goals over the last four season, Rodrigo Palacio ends his adventure with the Rossoblu," the club wrote in a statement.
“Bologna would like to thank Rodrigo for the extraordinary contribution he has made at the club, on and off the pitch, wishing him further sporting joys that a professional of his calibre deserves."
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