Mr Cuomo, 82, died of natural causes from heart failure, surrounded by his family at his home, on the same day his son Andrew started his second term as state governor.
He loomed large in New York politics as governor from 1983 through 1994 and became nationally celebrated for his ability to weave the story of his humble upbringing with ringing calls for social justice.
But he was also known for the presidential races he stayed out of in 1988 and 1992, agonising so publicly over whether to run for the White House that he was dubbed “Hamlet on the Hudson”.
In 1991 Mr Cuomo left a plane idling on the tarmac at Albany airport rather than fly to New Hampshire and jump into the battle for the presidential nomination at the last minute, leaving the door open for a lesser-known governor, Bill Clinton of Arkansas.
Mr Cuomo’s last public appearance came in November, when Andrew was re-elected governor of New York and the frail-looking patriarch and his son raised their arms together in victory at the election-night celebration.
He did not attend Andrew’s speech yesterday because he was not well, but the current governor spoke of his father.
“He is in the heart and mind of every person who is here. He is here and he is here, and his inspiration and his legacy and his experience is what has brought this state to this point,” Andrew Cuomo said.
“So let’s give him a round of applause.”
Mario Cuomo’s big political break came in 1982 when, as New York’s lieutenant governor, he won the Democratic nomination for governor in an upset over New York mayor Ed Koch and went on to beat conservative millionaire Republican Lewis Lehrman.
His reputation for eloquence was secured at the 1984 Democratic National Convention when he delivered his “Tale of Two Cities” keynote address, in which he told of the lessons he learned as the son of a grocer in New York City.
The electrified delegates in San Francisco cheered “Mario! Mario! Mario!” and some wondered whether they had chosen the wrong presidential candidate in Walter Mondale.
While Mr Mondale’s candidacy stumbled, Mr Cuomo took his oratorical skill to Notre Dame University, where as the nation’s most famous Roman Catholic supporter of abortion rights, he argued the church should not expect him to press for outlawing terminations, given that many Catholics themselves were having them.
US President Barack Obama said today Mr Cuomo was “a determined champion of progressive values and an unflinching voice for tolerance, inclusiveness, fairness, dignity, and opportunity”.
“His own story taught him that as Americans, we are bound together as one people, and our country’s success rests on the success of all of us, not just a fortunate few,” he said.
Mr Cuomo was an unusually cerebral politician, giving to musing at length about anything from fiscal policy to the Jesuit philosopher Pierre Teilhard de Chardin.
He was prickly as well as eloquent, regularly sparring with reporters, Republicans, fellow Democrats and even children.
He once said, “I didn’t come into this business to be bland” and he rarely was. Complaining about what he saw as anti-Italian stereotyping, he once said the Mafia was “a word invented by people” and “a lot of baloney”. He once had a little boy near tears after asking how old he was and then pressing the child on how he could be sure of that.
In early 1987, he was leading in the polls among prospective White House contenders when he said he would not be a candidate. A more protracted dance in 1991 ended with the filing deadline for the nation’s first presidential primary 90 minutes off.
Mr Cuomo walked into a packed news conference in Albany and cited a continuing budget battle with New York’s Republicans in declining to run. Before the news conference had even ended, the national TV crews were packing up their cameras.
Mr Cuomo easily won re-election for governor in 1986 and 1990, repeatedly vetoed legislation that would have restored the death penalty in New York and closed down the Shoreham nuclear power plant on Long Island. He also built 30 new prisons. Under him, the state budget grew from 28 billion to 62 billion dollars.
In 1993 he turned down an opportunity to be nominated by Mr Clinton for a seat on the US Supreme Court, telling the new president in a letter that “by staying active in our nation’s political process, I can continue to serve as a vigorous supporter of the good work you are doing for America and the world”.
Nineteen months later, with voters tired of him, Mr Cuomo lost his bid for a fourth term to George Pataki, a Republican state politician who had promised to cut taxes and bring back the death penalty.
Born in 1932, Mr Cuomo grew up behind the small grocery store run by his parents in New York’s Queens borough.
He graduated from St John’s Law School in 1956, tied for top class honours, and soon after went into private practice. He came to the attention of New York City’s political community in 1972 when he successfully mediated a housing dispute in Queens for then-mayor John Lindsay.
He lost a race for mayor of New York City to Mr Koch in 1977. During the campaign, posters that read “Vote for Cuomo, Not the Homo” mysteriously appeared in some neighbourhoods. Mr Cuomo denied any responsibility, but bachelor Mr Koch never forgave him.
Mr Cuomo and his wife Matilda had three daughters and two sons, Andrew and Chris, a CNN newscaster. His daughter Maria married designer Kenneth Cole.