The justices upheld rulings by a Family Court judge and Court of Appeal judges.
But - in a case which has led to calls for Britain's divorce laws to be changed - Mr Owens refuses to agree to the split.
He claims if their marriage has broken down it is because she has had an affair or is "bored".
She lives in a house the couple own next door to the marital home in Broadway, Worcestershire.
Even though the couple have not lived together since 2015, when Tini originally petitioned for a divorce, their relationship status didn't fit with the current divorce law in England and Wales.
The supreme court justices analysed the rival legal arguments, which revolved around concepts of "unreasonable" behaviour and "fault", at a hearing in London in May and delivered their ruling on Wednesday.
But Mr Owens' barrister Hamish Dunlop said Mrs Owens "was essentially advocating divorce by unilateral demand" and justices had rightly rejected her appeal.
Mrs Owens has been married for 40 years with two adult children, but said she'd been contemplating a divorce since 2012, when she consulted solicitors on what to do next.
Lady Hale, president of the Supreme Court, said while she found the case "very troubling" it was not for judges to "change the law".More news: Roseanne Barr says she's feels forgiven for her tweet scandal
Her colleague Lord Wilson said: "She must remain married to Mr Owens for the time being".
"The appeal of Mrs Owens must be dismissed".
In 2016 she failed to persuade Judge Tolson to allow her to divorce.
The Supreme Court (in contrast to the Court of Appeal) raised questions about whether the trial judge had heard enough evidence to determine the cumulative effect of the wife's allegations on her following just a one-day hearing and having only examined through oral evidence 4 out of her 27 allegations.
Another said Parliament had "decreed" that being in a "wretchedly unhappy marriage" was not grounds for divorce. They say the case is about "proper interpretation" of legislation.
Her lawyers said she shouldn't have had to prove that Hugh's behavior was "unreasonable" - and asked for a "modest shift" in interpreting the law.
Fiona Snowdon, family law expert at national law firm Simpson Millar said: "We are disappointed at this decision".
Supreme Court justices have now also ruled against her.
She claimed it had become a "loveless" marriage and accused him of authoritarian and demeaning behaviour, to the point that she could not reasonably be expected to stay with him. An incomprehensible idea in the 21st century and unreasonably paternalistic. Such measures have already been in regions such as Sichuan, Fujian and Guangdong provinces to counter a trend of divorces triggered by differences over trivial matters or that have been filed impulsively, according to Li Mingshun, a law professor at China Women's University.
"Divorce can be a painful, drawn out experience". If one partner objects, as Hugh did in this case, then the couple must live apart for five years before being granted a divorce.