Forensic anthropologist Francisco Etxebarria said that after a year-long search his team had positively identified in an alcove in a convent crypt "some fragments" of the "Don Quixote" author who died in 1616 a week after William Shakespeare.
Though there is no genetic proof of the find at this stage, Etxebarria's team of anthropologists and archaeologists said they were confident of the claim on the basis of the documentary research they carried out.
"After analysing all the information... It is possible to consider that amid the fragments of the 'reduction' discovered in the ground of the crypt of the current church of the Trinitarians are some fragments belonging to Miguel de Cervantes," Etxebarria said.
Cervantes is recorded as having been buried at the convent's chapel in the centre of the Spanish capital a day after his death on April 22, 1616, but the exact whereabouts of his grave were unknown.
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Etxebarria's team launched in April 2014 what is the first significant search for the remains of the greatest writer of the Spanish Golden Age.
Using infrared cameras, 3D scanners and ground- penetrating radar, they identified 33 alcoves where bones could be stored.
His influence on the Spanish language has been so great that the language is often referred to as "the language of Cervantes".
Cervantes was shot twice in the chest and once in his left hand during a 1571 naval conflict, the Battle of Lepanto, in which the Holy League led by Spain defeated the Ottoman fleet. His bones would still show signs of the injury.