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.
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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.
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.