Allen Morgan, 74, wanted Carole Morgan out of the way so he could start a new life with his lover.
A jury has now unanimously convicted him of conspiracy to murder.
The 36-year-old victim was found hacked to death at the convenience store she ran with her husband, then aged 31, in Linslade, Bedfordshire, on August 13, 1981.
At the time there was not enough evidence to charge anyone and Morgan was not considered a suspect, the Crown Prosecution Service said.
The case was reopened in 2018 following a review by a cold case team.
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