Stuart Paul Anderson denied any involvement in the murder of Vicki Ramadan, after finding her body inside her home at Sydenham in Melbourne's northwest in March 2019.
He told media in television interviews that she seemed like a lovely lady and that he hoped "the cops catch the son of a bitch" who did it.
A jury on Thursday found it was him who had murdered her.
Prosecutors had alleged Anderson killed Mrs Ramadan between March 23 and 25, 2019.
The pair met when the widowed Mrs Ramadan knocked on Anderson's door and asked for his help with some odd jobs around her home, including building flat pack furniture.
Witnesses claimed to have heard multiple arguments between the pair in the days before Mrs Ramadan was killed.
On the morning of March 23 a taxi driver said he saw Mrs Ramadan and Anderson arguing about him arriving late to help her with some work.
About 3.30pm a witness heard Anderson aggressively yelling at Mrs Ramadan, telling her "f*** you, fix it yourself".
He left and arrived home "scary" angry, a woman living with him at the time said.
At 6pm Anderson was back working at Mrs Ramadan's.
There were signs of life until lunchtime on March 25, including a call from one of her phones to another and an electricity spike consistent with a hotplate, and then nothing.
The jury that convicted Anderson was the third he faced over the allegations.
One jury was discharged after being unable to reach a verdict and a second trial was discontinued before deliberations were reached.
In those hearings jurors in the Victorian Supreme Court were told Anderson told his partner he was going to check on Ms Ramadan about 9am on April 6, 2019 and to pick up some tools he had left at her house.
He said he found her body after going through the back door, which had been kicked open.
When police became suspicious about his involvement he confessed he had actually discovered her body between 1.30am and 2am on April 6 after he himself knocked in the back door.
Prosecutor Neil Hutton described the story as a sham and a charade.
The court heard Mrs Ramadan was known for wearing lots of jewellery, which was found alongside cash in her home after she was killed.
Supporters of Mrs Ramadan were in court for the verdict, including one who gave Anderson the middle finger after the guilty finding was read.
Anderson will face a pre-sentence hearing at a later date.
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