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After leaving the bar, the 34-year-old climbed an electrical tower, was hit by a shock and plunged 30 metres (100 feet) to the ground.
He died that evening in hospital, press reports said.
According to a report in the ABC daily newspaper, citing witnesses, the man told friends in the bar in Cordoba, southern Spain, on Sunday, that he had decapitated his 30-year-old partner.
But he was so calm they did not believe him, despite bloodstains on his shirt.
"A while later when several customers left the bar and saw a pool of blood in the road, they immediately realised this was not a macabre joke. Horrified, they discovered a bag near the bar, inside of which was the victim’s head," the ABC daily said.
Police confirmed they had found the woman's body with knife wounds, and that her suspected killer, identified only by his initials MRTR, had fallen from the electrical tower, later dying in a Cordoba hospital.
Near the tower they found a knife believed to be the murder weapon, said a Cordoba region spokeswoman for the national police, Rosa Ortiz.
Police were unable to provide details about the murder because they were interviewing witnesses and had yet to file a judicial report, expected Wednesday, she said.