According to the newspaper, Albuquerque police were called to Tapia’s house on Sunday evening by a family member who found a body there.
Police spokesman Robert Gibbs told the Journal that the death did not appear suspicious and an autopsy would be conducted to determine the cause of death.
Tapia, 45, was known for his battles with cross-town rival Danny Romero, Paulie Ayala and Marco Antonio Barrera.
He earned world titles in the super flyweight, bantamweight and featherweight divisions in a professional career that began in 1988.
In 2007, Tapia was hospitalised after an apparent drug overdose. While he was in hospital, two members of his family — his brother-in-law and a nephew — were killed in a road accident.
Tapia, whose battles with addiction led to several brushes with the law, amassed a record of 59 wins, five losses and two draws with 30 knockouts.
Tapia’s last fight was an eight-round unanimous decision over Mauricio Pastrana in Albuquerque in June 2011.