George Metcalff, 71, killed Patricia Henry, 46, known as Patti, at her flat in Girvan, South Ayrshire, on November 13, 2017.
Prosecutors claimed Metcalff, known as Kenny, attacked Ms Henry by "means unknown."
Her body has never been discovered despite extensive searches in the Girvan area.
Metcalff made several trips to Ms Henry's flat following her murder including in a hired van apparently to collect a mattress and bed frame late at night.
He also ceased constant phone contact with Ms Henry after her murder date despite the pair making 143 calls that month.
Metcalff faces a life sentence after he was found on Thursday of murdering, raping, physically and indecently assaulting her after a 10 day trial at the High Court in Glasgow.
He was also convicted of attempting to defeat the ends of justice as well as raping and physically assaulting two other women between 1971 and 2004. There were shouts of: "Yes" and crying from the public gallery as the jury delivered its verdict.
Metcalff was remanded in custody pending pending background reports for sentencing next month.
Judge Lord Armstrong said Metcalff was convicted of a "series of the utmost offences" before putting him on the sex offenders register.
Jurors heard Ms Henry first met Metcalff in 2008 when she moved into the flat above his in Burnfoot Crescent, Paisley.
She went on an extended holiday to Gran Canaria before returning to the area when they began constant contact. Metcalff became the guarantor for her new flat in Girvan in October 2017 and paid her deposit as well as her first month's rent totalling £700.
The trial was told the pair made 54 texts and 143 calls to each other between November 1 and 13 - the day of the murder.
Metcalff made a final two calls to her on November 14 which went to voicemail before he stopped contact with her.
Prosecutor Alex Prentice QC told jurors in his closing speech that based on the evidence from witnesses, Metcalff had "control" over Ms Henry.
He later stated: "This was an extemely vulnerable person who is someone I suggest Metcalff took advantage of.
"Metcalff murdered Patti and disposed of items linked to that murder to conceal and destroy evidence to avoid detection, arrest and prosecution.
"As we know, Patti has never been found and on the evidence, the last person to have ever seen her is Metcalff.”
The trial was told Metcalff ran an errand for Ms Henry, checked her bank balance and withdrew £250 on the day of her murder.
He hired a van the following day which he claimed was used to collect and dump an old matress and bed frame belonging to her.
Metcalff told jurors that he had no contact with her on that day.
Following the verdict Detective Superintendent Suzanne Chow said: “George Metcalff’s conviction brings to an end his 50-year reign of abuse against women which culminated in his murder of Patricia Henry.
“Throughout the investigation and trial Patricia’s family have conducted themselves with dignity and determination to find Patricia.
“It is now up to George Metcalff to do the decent thing, to tell us where Patricia’s body is and to allow her family to give her a proper burial and to mourn.”