Valerie Graves, 55, was found dead in a bedroom of a waterside property in Bosham, near Chichester, West Sussex, on December 30.
Sussex Police said a man had now been arrested and was being held in custody.
The victim and her family had been looking after the house while the owners were away over the holiday period.
Her son Tim Wood previously paid tribute to his mother and pleaded for information about the killing.
Ms Graves and her family were looking after a house in the quiet village
He said: "My mum was much loved and will be sorely missed by the whole family. She was a free spirit who enjoyed her life and was a talented artist.
"She had lived in Scotland for about 10 years, a place she loved and which inspired her passion for art."
He added: "This has been devastating for the family and has come as a complete shock.
"We would appeal to anyone who has any information about this, no matter how trivial it is, to contact the police to help us catch whoever has done this horrible act."
The victim's children made an appeal for information about the killing
Ms Graves, who had recently moved back to Sussex from Scotland to be closer to her family, was house-sitting at the property with her mother, sister and her sister's partner while the owners were abroad.
Police said she went to bed at 10pm on Sunday, December 29 and was found dead by one of her three relatives at around 10am the following day in the bedroom where she had been sleeping.
A post-mortem examination revealed she had suffered significant head and facial injuries, but detectives have not confirmed whether a weapon had been used.
The death shocked the small community of Bosham, which featured in an episode of the ITV crime drama Midsomer Murders.