He then dumped the pieces in a lake at Jillelaguda of Meerpet, a senior official was quoted as saying by The Hindu.
He confessed on Wednesday amid searches for 35-year-old Venkata Madhavi, who was reported missing on January 18.
According to the police, 45-year-old Guru Murthy, a native of Prakasam district in Andhra Pradesh, arrived at the Meerpet police station and confessed to killing her.
The man has been arrested and a detailed probe is underway.
After his stint in the Indian Army, Murthy began working as an outsourced security guard with the DRDO in Kanchanbagh.
Murthy accompanied his in-laws to the police station to lodge a missing complaint about his wife.
He was allegedly supporting the police in searching for her when the police, based on suspicion, questioned him.