The Galway West TD, was first elected as a Fianna Fáil TD in 1965 and went onto serve in Leinster House for almost 40 years.
Mr Molloy, who died aged 80, served as minister for local government, minister for defence, and minister for energy.
He was a founding member of the Progressive Democrats along with Des O’Malley and Mary Harney in 1985, and went on to negotiate for the party during government coalition on a number of occasions, including with Fianna Fáil in 1989 .
Sending condolences to his wife Phyllis, his daughters Sorcha and Sinead, and sons Donnacha and Dara, President Higgins said Mr Molloy had “earned the respect of both his supporters and opponents because of the integrity with which he held his views”.
“Bobby Molloy made a huge contribution to Irish public life as a member of several Cabinets,” he said of the former Galway mayor.
“The constituency he represented was one of the largest in the country, containing Ireland’s largest Gaeltacht, the Aran Islands, and Inishbofin.
“Throughout his career, he gave excellent service over several decades, and his name is recalled with great affection throughout the constituency. His life in politics began before mine, and on every platform he served, he delivered his contribution, which was always well-informed, with great distinction.”
Taoiseach Enda Kenny also paid tribute to Mr Molloy who retired from politics in 2002.
“Bobby gave a long and dedicated service in many Ministries and he was always a tireless campaigner for his native Galway,” the Taoiseach said.
“I got to know Bobby well during his time in the Dáil and I extend my deepest sympathy to his wife Phyllis and to their family.”
Fianna Fáil leader Micheál Martin described Mr Molloy as “a man of great personal warmth, integrity and purpose”.