De Rossi played only seven matches for the Buenos Aires outfit, scoring once, but said he needed to return home for family reasons.
"I need to go home. I'm leaving Boca and football," said the 36-year-old former Italy and Roma midfielder.
"I'm leaving a club that has entered my heart, this sport, my passion".
De Rossi, who suffered several injuries during his time in Argentina, insisted that he has "no serious health problems" but merely felt "the need to be closer to my family, to my daughter. I miss them and they miss me".
De Rossi spent 18 years at Roma before leaving the club at the end of last season.
He played 117 times for Italy from 2004-17 and won the World Cup in 2006.