Researchers in Edinburgh discovered the actress is 19 generations removed from Bruce, who liberated his country from English rule.
And it emerged 48-year-old Swinton, who has won acclaim for her roles in The Curious Case of Benjamin Button, Burn After Reading and Vanilla Sky, is related to Bruce through both her father and mother.
Researchers at the ScotlandsPeople Centre, a family history research centre in Edinburgh, traced the actress's bloodline from her parents, Sir John Swinton of Kimmerghame, Berwickshire, and Judith, Lady Swinton, who was born in Australia, to the Scottish king who died in 1329.
Both of Swinton's parents share a common descent from Robert II, Bruce's grandson.
The Swintons descend from Robert II's illegitimate son, the Duke of Albany, while Lady Swinton descends through her Balfour ancestors from the child of Robert II's favourite mistress, Mariotta Cardney.
Swinton's family tree also includes a 17th Century renegade preacher, Gabriel Semple, a Victorian Archbishop of Canterbury, Archibald Campbell Tait, and an East India Company soldier, Archibald Swinton.
The London-born actress, who now lives in Nairn, may have inherited her stage talents from her great grandmother, singer and society hostess Elizabeth Ebsworth.
The Swinton family tree also features scientist Alan Archibald Campbell Swinton, who took the first X Ray pictures in Britain, and Major General Sir Ernest Swinton, who helped develop the tank.
The actress is the latest subject of the ScotlandsPeople Centre's series of exhibitions, Famous Scots.
She is the fifth in a series of six special exhibitions which explore the ancestry of a famous Scot, looking at the ancestors and how they lived.
Comedian Billy Connolly, scientist Sir James Black, Garbage singer Shirley Manson and actor Brian Cox have also been the subject of the series.
George MacKenzie, keeper of the records at the National Archives of Scotland, said: "These exhibitions are proving popular, giving people a much more individual insight to our shared past and some of our biggest stars' family stories.
"These stories are inspiring and fascinating, and they are available to everyone for free."
Marie Christie, project director of Homecoming Scotland 2009, who are supporting the exhibition said: "Ancestry is a key theme for Homecoming Scotland and visitors to the exhibition can see not only Tilda Swinton's family history but learn how to undertake their own genealogical research."
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