Rosemary Broadwell, 76, went missing on September 15th in Algorfa, an area on the Costa Blanca near Alicante that is popular with expatriates.
Her companion Charlie Bevill-Warcup reported her missing at the time and an appeal was launched by her family. Her granddaughter Lisa had appealed for information on Twitter.
"We have only just found out the horrible news," Cheryl Webster, the daughter of the victim, told The Local.
Confirming that Mr Bevill-Warcup was being held for the murder she said: “He lived with her, but he is not my father and was not married to her,” she said. "It’s come as a horrible shock, we are waiting to find out more."
Detectives from the paramilitary Civil Guard at Algorfa arrested Bevill-Warcup last night after he reportedly confessed to killing his partner.
Reports in Spanish newspaper El Mundo said that under questioning on Monday he had told the officers investigating Rosemary's disappearance, that he had beaten her with a blunt instrument.
On Tuesday he took officers to an area of scrubland where her decomposed body was discovered.
A postmortem confirmed that she had been beaten to death.
Bevill-Warcup had reported his partner missing, telling police that she had disappeared after he dropped her off at an ATM at the Ciudad Quesada urbanization near her home.
A missing notice drawn up by her daughter Cheryl described Rosemary - known to her friends as Rosie - as "4 ft 8 inches tall and a fit, well and able-bodied lady".
"Rosie is slim and has short blonde hair with red/purple high-lights. She has a tattoo of a tiny coloured lizard on her foot and another of a dolphin on her right shoulder," the missing notice read.
"Another distinguishing feature is that Rosie always has perfectly manicured finger nails."