The Italian midfielder signed a one-year deal with Boca in July after his contracted with boyhood club AS Roma expired.
De Rossi had a 19-year association with the Serie A club, making 615 appearances for the senior side, scoring 63 goals.
However, his time with his boyhood team came to a somewhat acrimonious end in May of this year when the Giallorossi offered him an off-the-field role instead of an extension on his playing contract.
Speaking to ESPN about his move to the Buenos Aires club, De Rossi said that "with each day I realize I made the best decision I could have."
The 36-year-old has travelled with the rest of the Boca squad to Ecuador for Wednesday's Copa Libertadores quarterfinal first leg clash against LDU Quito.