The 45-year-old stood trial before the Victorian Supreme Court accused of murdering Samantha Fraser, whose body was found hanging from a noose at her Phillip Island home in July 2018.
A jury found Basham guilty on Thursday.
The pair met in late 2005 and married in 2007 before having three children together.
But after years of domineering and controlling behaviour, prosecutor Nanette Rogers SC said, they separated in 2017, with Ms Fraser taking out intervention orders against him.
Basham then turned up at her Cowes home and waited for 90 minutes, while she dropped their children at school and had coffee with a friend at a local cafe, before killing her.
"He strangled her with rope and then hanged her with the rope from the garage door," Ms Rogers told the jury in her opening remarks.
"The accused then set about manipulating the crime scene to make it appear as though she killed herself."
Basham had threatened Ms Fraser after they separated, the prosecutor said, warning her that violent criminals could easily break into her home.
He also told her "if I can't have you then no one will".
The 38-year-old changed her locks and deleted a location app on her phone which she thought Basham was using to track her.
Basham also told one friend "just you wait and see, I'll get her", the prosecutor added, while telling another friend he could follow her location through her phone bills, still linked to his account.
In the weeks before her death, Ms Fraser told friends she felt unsafe and feared vindictive behaviour from Basham.
Defence barrister Ashley Halphen said the fact Basham assaulted Ms Fraser on the day she died - and therefore breached his intervention order - was not in dispute.
But the 45-year-old man denied murdering his ex-wife, with Mr Halphen arguing Ms Fraser took her own life after Basham left her home.
Basham is expected to return to court on September 19.
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