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.
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 in police custody."
A report is to be sent to the procurator-fiscal.