The ruling follows a long-running controversy over the writer's war-time broadcasts from Germany.
In the Dublin High Court, counsel for The Irish Times, John Gordon, said it accepted that Stuart "never expressed anti-Semitism in his writings or otherwise and regretted the publication of any impression to the contrary".
The newspaper is to pay Stuart's legal costs following the libel action over an article published in October 1997, which followed critical television documentaries about Stuart shown on Channel 4 and RTE, the Irish television network.
The issue of whether Stuart was anti-Semitic caused a split in Dublin's literary world and led to bitter disputes over his membership of Ireland's arts academy, Aosdana, to which he was elected in 1983. It echoed the controversy surrounding the writer PG Wodehouse, who made broadcasts for the Germans during the war.
Stuart was jubilant after yesterday's settlement. He said: "My last novel was Redemption, and now I feel redeemed. I feel on top of the world. The flood-water is rising all the time but I am rising even quicker. It's over now, thank the Lord."
Stuart, an Irish nationalist who took the republican side during the 1922-23 civil war, lived in Germany during the Thirties before returning to Ireland. In Germany, he broadcast in English to Irish audiences, leading to the controversial allegations.
Ulick O'Connor, a biographer, said accusations of anti-Semitism against Stuart were "scurrilous". He said the writer's broadcasts had been largely restricted to literary subjects, and that when he was pressed to make political statements he had ceased to make the broadcasts.
"They wanted him to condemn the Russians, and he wouldn't do that. Stuart is a major writer and this has all been deeply unfair," he said.
The poet Paul Durcan, who joined Stuart and O'Connor in court, said: "This has been going on for 30 years and has obviously caused Francis great pain. The outcome was a great relief and a great vindication."
Besides his writings, Stuart enjoyed a degree of celebrity through his marriage to Iseult, the daughter of Maud Gonne, the society beauty and nationalist who broke the poet W B Yeats' heart by marrying John McBride. Iseult was also engaged to the poet Ezra Pound at one time.
Ms Gonne's son, Sean McBride, was at one time the IRA's chief of staff, and in 1974 won a Nobel peace prize for his work as United Nations assistant secretary-general .
Yeats once awarded the young Stuart a gold medal for poetry, praising his "cold exciting strangeness" and "single dominating aim".
He said he saw Stuart as a future leader of a new Irish literary renaissance.Reuse content