Jean Campbell, 53, was last seen heading towards Cranhill Park while walking her dog within sight of her home in the east end of Glasgow on Friday December 13.
Her body was discovered the next morning by her husband who, on returning from his night shift, realised she was not home and went to look for her. The family's German Shepherd Kai was found in the park.
Police said the 53-year-old had suffered a particularly violent attack and a reconstruction of the case featured on the BBC's Crimewatch programme.
A 21-year-old man has now been arrested in connection with her death, police said today.
A second man, aged 22, has also been arrested in connection with allegedly attempting to pervert the course of justice in relation to the investigation.
A Police Scotland spokesman said: "Following a police operation in Glasgow, Friday July 11, a 21-year-old man has been detained and subsequently arrested in connection with her death. He is presently detained in police custody.
"A second man, aged 22 years, also from Glasgow, was detained and has been arrested in connection with allegedly attempting to pervert the course of justice in relation to this investigation. He too is presently detained in police custody."
A report is to be sent to the procurator fiscal.
More than 1,500 DNA samples have been taken during the investigation into Mrs Campbell's death.
During an appeal last month Detective Chief Inspector Colin Carey, the officer in charge of the investigation for Police Scotland, said: ''Jean's family are devastated by the loss of their wife, mother and grandmother and they deserve answers.''