Quezada, 43 and originally from the Dominican Republic, broke down during police interrogation on Tuesday and confessed to first hitting and then strangling her partner Angel’s son.
The main suspect in the investigation told police she acted alone, Spanish radio station Cadena Ser reported.
The former butcher, who raised police suspicions after she claimed to have found a T-shirt belonging to little Gabriel in an area they had already combed, admitted she hid all of her victim’s clothes in a nearby rubbish tip.
Spanish police have been monitoring Quezada for the past week, suspicious of her overdramatic behaviour and unrelenting interest in carrying out TV interviews.
It is understood that on Sunday Spain's Civil Guard followed her to Gabriel's grandmother's country house and covertly filmed her as she removed the child's body from a well and put it in the boot of her car.
Authorities proceeded to arrest Quezada as she parked her vehicle outside her apartment.
Gabriel's father Ángel isn't a suspect at present, according to police sources.
An autopsy carried out on the child found the cause of death to be strangulation.
Spanish daily El País reported on Monday that authorities have begun looking into Quezada's criminal records and found that she was a previously suspect in the death of her four-year-old daughter, who fell out of a window in an apartment block in 1996, but a court later ruled the child's death accidental.
Police have since reopened the case in the hope of finding answers to the unexplained circumstances in which the minor died.
Spanish daily El Mundo interviewed the family of one of her ex-boyfriends in Burgos, a man twenty years her senior.
“She only cares about money and getting what’s best for her,” they said of Quezada, who attempted to marry her boyfriend on his deathbed to claim his life insurance.
Gabriel’s disappearance has gripped the nation ever since a missing person's alert with a photo of him smiling went viral on WhatsApp, Facebook, Twitter and other social media.
Hundreds of officers were mobilized in the search for 'El Pescaíto' (the Little Fish) after he went missing on February 27 in the southeastern village of Las Hortichuelas, near Almería.
A picture of a blue fish, inspired by Gabriel's love of the sea, was widely shared under the hashtag #TodosSomosGabriel, “We're all Gabriel” in Spanish.