The 81-year-old served one of the shortest terms on record as leader of the country but his tireless work on the Northern Ireland peace process secured his legacy.
Mr Reynolds was a businessman, showband promoter, politician and deal-maker and is credited with laying the ground work for lasting peace.
Taoiseach Enda Kenny expressed his sympathies with the family and paid a glowing tribute to the former leader’s time in office.
“Albert Reynolds brought an energy and drive to the development of business and economic growth during his tenure in office as minister for industry and as minister for finance,” he said.
“As taoiseach, he played an important part in bringing together differing strands of political opinion in Northern Ireland and as a consequence made an important contribution to the development of the peace process which eventually led to the Good Friday Agreement.”
Mr Reynolds’ elder son Philip confirmed to RTE he died overnight.
The family confirmed last year that he had been suffering from Alzheimer’s disease.
Mr Reynolds is survived by his wife Kathleen, two sons and five daughters.
Sinn Fein leader Gerry Adams expressed his condolences.
“I’m really sorry to hear of the death of Albert Reynolds,” he said.
“Albert acted on the North (of Ireland) when it mattered.
“My thoughts are with Kathleen and all the Reynolds family. May he rest in peace.”
Bertie Ahern, who succeeded Mr Reynolds as Fianna Fail leader and taoiseach in 1994, said Mr Reynolds’ role in the Downing Street Declaration was a critical point in the road to peace.
“If there hadn’t have been a Downing Street Declaration, I don’t think there would have been a (IRA) ceasefire in the first place,” Mr Ahern said.
Northern Ireland Deputy First Minister Martin McGuinness told BBC Radio Ulster: “I think Albert Reynolds showed tremendous courage, Albert was a peacemaker.
“He was someone who understood the North and the nationalist republican community but, just as importantly, he understood the loyalist unionist community and had contacts in both.”
The Sinn Fein leader said the former taoiseach was a key player in the peace process.
He said: “Albert Reynolds played a really important role in paving the way for what is arguably the most important development in 20 years, maybe even 100 years, and that was a decision by the IRA leadership to call a ceasefire in 1994 which so dramatically changed the security and political situation here on this island and particularly in the North.”
Former taoiseach and ex-Fine Gael leader John Bruton – once dubbed “John Unionist” by Mr Reynolds – laughed off the jibe and paid tribute to his predecessor.
“His particular contribution, I think, is the negotiation of the Downing Street Declaration, it was absolutely crucial,” he said.
David Cameron said: “I’m sad to hear of the death of Albert Reynolds. His partnership with Sir John Major led to the crucial Downing Street Declaration in 1993.”
One of the most symbolic gestures in Mr Reynolds’ short time as Taoiseach was a public handshake he instigated between Mr Adams and former SDLP leader John Hume following talks in Government Buildings in Dublin in 1994.
Mr Reynolds attempted to take the role of taoiseach in 1991 in a failed motion of no confidence in his then-party leader Charlie Haughey.
Subsequently, his time at the head of government was dogged by controversies.
Mr Reynolds had to contend with the X Case, which strained political relations and caused deep division in Irish society after a rape victim was initially refused the right to travel for an abortion.
Other crises included the Beef Tribunal, which examined malpractice in the industry, including Mr Reynolds’ connections to beef magnate Larry Goodman.
Mr Reynolds’ first coalition, a deal with the Progressive Democrats, collapsed late in 1992.
Following elections, a new government was agreed between Fianna Fail and Labour but despite Mr Reynolds’ internationally-recognised peace process efforts, issues closer to home shattered any long-term ambitions.
The mishandling of the Smyth extradition brought down his second government in November 1994. The delay in acting on the request from authorities in Northern Ireland to prosecute the abuser sparked the ultimate crisis.
On his departure, Mr Reynolds famously remarked: “It’s amazing. You cross the big hurdles and when you get to the small ones, you get tripped up.”
Fianna Fail leader Micheal Martin praised Mr Reynolds’ enduring legacy as a peacemaker.
“There were many, many cynics at the time who thought he was going down the wrong route and felt he was being overly-optimistic,” he said.
“I think the key was the development of a very strong relationship, a personal relationship, with (then British prime minister) John Major.
“The trust that developed between the two of them, I think, was instrumental in bringing the British-Irish governmental approach to the issue.
“It was key also in terms of reaching out to the republican movement and the loyalist movement.”