Natalia Wilkanowska, 50, disappeared in 2003 after travelling to visit her ex-husband Gerald Doherty in Luton.
Her body was found in December 2015, Luton Crown Court was told.
Mr Doherty's brothers, Joseph and Daniel, are on trial accused of helping conceal her remains and lying to police.
The court heard Natalia was last seen by her children in April 2003 when she left her Eastbourne home to travel to Luton.
Prosecutor Neil King said her ex-husband was responsible for her death. The couple had separated in 2001 after 23 years of marriage.
Mr Doherty took his own life at a flat in Port Glasgow, Renfrewshire, on their wedding anniversary in July 2003. He had been receiving psychiatric care.
His two brothers, who both wore hearing loops in the dock, face a total of seven charges.
Natalia's death came to light in 2014 when Joseph Doherty revealed Gerald had murdered her, but that her remains had been "chopped up".
Mr King told the court Natalia's body was found a year later - intact - under rubble in the garden of Daniel Doherty's house in Icknield Way, Luton.
She had suffered "a blunt force trauma" inflicted by a third party, but the cause of death could not be established.
Read more on this and other Bedfordshire stories
Mr King said Daniel Doherty, who worked as a builder, must have "connived in the deposition of the body".
He said both men lied to the police and obstructed the coroner.
Daniel Doherty, 67, of Icknield Way, Luton denies two charges of perverting the course of justice and two charges of obstructing the coroner, by aiding and abetting the concealment of a body and lying to police.
Joseph Doherty, 73, of Old Greenock Road, Port Glasgow, denies perverting the course of justice and obstructing the coroner by giving a false account of her death.
Both men also deny preventing lawful burial.
The trial continues.

In a study of more than 70,000 women, optimists were less likely to get fatal cancer, heart disease, lung conditions and stroke in their retirement years.
Although some of the association is explained by healthier life choices and behaviours, experts believe a positive mental attitude is powerful in itself.
And even if you lack a natural sunny disposition, optimism can be learned.
Encouraging people to imagine a bright future could be a good medicine to boost public health, say the authors of the study in the American Journal of Epidemiology.
The researchers looked at health data collected from a large US study of working and retired female nurses.
The participants had been asked to rate how optimistic they perceived themselves to be on a scale of zero to 24.
The healthy women, who ranged in age from 58 to 83, were monitored over the next eight years and any disease-related deaths were recorded. There were 4,566 deaths overall.
Higher optimism was linked with lower death risk, even after controlling for other factors such as whether the woman was married, came from a richer or poorer family background, or had a history of diabetes, high blood pressure, high cholesterol or depression.
A significantly lowered risk was seen for deaths from a number of causes, including heart disease, stroke, cancer, respiratory disease and infection over the course of the study period.
The researchers believe optimism may have a biological effect on the body as well as a psychological one, although they didn't look at this.
Other studies have linked a positive outlook to lower inflammation, for example, and better heart health.
Join the conversation - find us on Facebook.
Investigator Dr Eric Kim, from the Harvard TH Chan School of Public Health, said there were several strategies people might want to try for an optimism boost:
Or you could try a course of mindfulness or some sessions of talking therapy.
He said: "Twin studies suggest up to 25% of optimism might be genetic or inherited which would mean up to 75% could be modifiable."
A woman's body lay under builders' rubble in a back garden for more than 12 years before it was discovered, a jury has heard.
[NEXT_CONCEPT]
Women who look on the bright side of life cut their risk of many deadly diseases, according to researchers.