The Herald reported that Mark Townson met Mrs McDowell and her late husband while working as a branch-based financial adviser.
He worked for Legal and General for 18 years and between 2002 and 2013 advised the couple, who had £1.4 million across various accounts, while working at a Virgin Money branch.
Townson said he was in "a desperate financial situation" caused by him running three households.
His was caught by a branch manager in December 2012 when he took another £80,000 from the McDowells' Virgin Money account and paid it into an account in his own name at the same branch.
Townson claimed that the money had been given to him by the childless couple as a "gift" due to his financial situation.
Giving evidence, he said:
"They were not extravagant in their spending, they didn't go on holiday and they didn't have any kids. I'd say we became friends - I got Christmas cards and birthday cards from them.
"In 2008 or 2009 Mr McDowell began to deteriorate. Mrs McDowell got more control after that. Everything was in files, it was really organised. I thought I'd done as good a job as I could possibly do for them."
Mrs McDowell was adamant she never gave Townson any money or agreed to him investing cash on her behalf.
The jury took just 56 minutes to convict him.
Graeme Tones, a Virgin Money spokesman, said:
"At Virgin Money we take the safety and security of our customers extremely seriously and the vigilance of our Giffnock colleagues has helped to identify this appalling crime."
A Legal & General spokesman said:
"This shouldn't have happened. When it was discovered, we reported it to the police, apologised to Mrs McDowell, and ensured she got all her money back."
