Ms Quill died at Marymount University Hospital and Hospice in Cork on Thursday.
She is survived by her nephews, grandnephew and grandniece.
Her Requiem Mass will take place at St Patrick’s Church on the Lower Glanmire Road, Cork at 10am on Saturday.
She will be buried at St Garvan’s Cemetery in Kilgarvan, Co Kerry.
Ms Quill – a native of Kilgarvan, Co Kerry – was initially involved in Fianna Fáil but was best known as one of the longest serving Progressive Democrat TDs.
Ms Quill joined Des O’Malley and Mary Harney in setting up the Progressive Democrats in 1985. She was a party candidate in Cork North Central in the 1987 General election and was one of 14 PD’s who were elected to the 25th Dáil.
She served as a TD for Cork North Central from 1987 to 1997, winning election on three occasions (1987, 1989 and 1992).
Ms Quill then served in the Seanad from 1997 to 2002 before opting not to contest the 2002 General Election.
A school teacher, one of her best known political anecdotes was being sent home during the count for one general election after being told she was going to lose her seat.
However she was called back to the count centre after a dramatic swing in transfers resulted in her successfully holding her seat.
Ms Quill was a member of Cork Corporation (now City Council) for 30 years from 1979 to 2009.
Despite the pleas of many independent Cork politicians, she never got to serve as Lord Mayor of Cork as the PDs were not part of the Fianna Fáil-FineGael-Labour mayoral pact.
Her longtime PD colleague Pearse Wyse did serve as Lord Mayor when he was previously a member of FF.
The Taoiseach hailed Ms Quill for her contribution to Cork and Irish life.
“I was deeply, deeply saddened to learn of the passing of Máirín Quill, someone who served the people of Cork with great distinction as a city councillor, senator and a deputy in Dáil Éireann,” Mr Martin.
“Erudite and impactful, Máirín championed the arts and culture in the city of Cork. I served on many boards with her, but I particularly enjoyed our time together on the arts committee of Cork Corporation.
“Máirín was a true renaissance figure with a great sense of the future of our city. She was always very helpful in providing advice and creative ideas.
“She was a true patriot and it was an honour to be her friend and colleague. My deepest sympathies go to all her family and friends. Ar dheis Dé go raibh a hanam.”
Tributes have also been paid by Cork City Council, business groups, art associations and particularly education groups across Ireland.
Ms Quill initially qualified as a primary school teacher having attended Mary Immaculate College in Limerick.
However, she secured a degree in English and History from University College Cork (UCC) and went on to teach at St Vincent’s secondary school in Cork.
Years after her retirement, she proudly attended school events as well as educational campaigns around Cork.
During her long career, she became particularly close to PD leaders Des O’Malley and Mary Harney.