Michael Finucane, the dead lawyer's son, said he was contacted by Canadian Judge Peter Cory on Monday who informed him of his decision to recommend an inquiry.
Finucane said his family would ask Belfast High Court on Tuesday to make public the findings of Cory's report on the killing of his father, who was shot by Ulster Defence Association gunmen.
The Finucane killing was one of the highest-profile in 30 years of violence in Northern Ireland between Catholics seeking to end British rule and Protestants committed to preserving it.
The death has been surrounded by accusations against the British security forces of collusion with the Protestant paramilitaries who shot the lawyer in front of his wife and children in their Belfast home in 1989.
The British and Irish governments asked retired Canadian Supreme Court judge Peter Cory in 2001 to investigate eight killings, including Finucane's case.
The judge presented his findings last October to the governments in London and Dublin, who had promised to hold inquiries if he recommended it.
Ireland published Cory's reports on the two cases in its jurisdiction last month.
Stevens said police could have
prevented Finucane's death
It said there would be an inquiry into accusations that Irish police colluded with the Irish Republican Army in killings of two Northern Ireland policemen in 1989.
But Britain's Northern Ireland Secretary Paul Murphy has not yet made the other reports public, saying his government needed more time to consider the legal and security implications.
Last year the European Court of Human Rights in Strasbourg ruled Britain had not adequately investigated claims Finucane was set up by members of its intelligence services.
A separate report from London police chief John Stevens said security forces could have prevented his killing.
Cory also investigated the killing of Rosemary Nelson, another high-profile Catholic lawyer killed by a car bomb blamed on the Protestant Loyalist Volunteer Force (LVF) in Lurgan in 1999.
Other cases he investigated include Robert Hamill, a Catholic kicked to death by a Protestant group in Portadown in 1997; and Billy Wright, the LVF leader shot and killed by the Irish National Liberation Army inside the Maze prison six years ago.
A source familiar with the findings said the judge had recommended inquiries in all cases.