It is believed John Campbell could not face living any longer in the flat in Bellrock Street, Cranhill, that he shared with his wife of 34 years.
He found his wife's body in Cranhill Park - just minutes from the flat - after coming home from work to discover she was missing.
Mr Campbell, 55, is understood to have heard the couple's German Shepherd, Kai, barking from across the road in the park.
Mrs Campbell, 53, a former restaurant waitress, had been brutally attacked as she walked her dog.
Detectives are still working to establish a motive for the killing.
She was spotted on CCTV at 10.30pm on December 13 near the park, wearing pyjama bottoms and a black puffer style jacket with a black hood.
Her body was found at about 7.30am the following day.
Anyone with information is asked to call police on 101.