She joined the national broadcaster in 1974, where she worked initially as a continuity announcer before becoming a programme presenter.
She won a number of awards for her work, including Radio Journalist of the Year 1988.
The 69 year old was the original presenter of Radio 1's Live Line programme before she moved to a slot vacated by Gay Byrne in 1999.
In 2005, the show moved to weekends.
She also presented a number of television shows, such as "Consumer Choice" and the Garda investigation programme "Crime Line".
In a statement this evening Director General Dee Forbes said that 'we learned today of the sudden passing of Marian Finucane with profound shock and sadness '.
She died suddenly at home and is survived by her husband and son.
President Michael D Higgins says it's with great sadness that her learnt of her death.
He says Ireland has lost a deeply respected, trusted and much-loved broadcaster.
Taoiseach Leo Varadkar says he's also stunned and deeply saddened to hear of her death.
He describes her as a true broadcasting legend who reshaped current affairs radio in Ireland.
Books of condolence have opened at RTÉ and Kildare County Council offices in Naas, for people wishing to pay tribute.