Bellow, 89, died on Tuesday at his home in Brookline, Massachusetts, with his wife Janis and five-year-old daughter Naomi at his side.
The bootlegger's son who became the Nobel Prize-winning author of Herzog and Humboldt's Gift, had been in declining health, but was "wonderfully sharp to the end", said his close friend and lawyer Walter Pozen.
Few writers have been so honoured in their time. He won three National Book Awards: in 1954 for The Adventures of Augie March, in 1965 for Herzog and in 1971 for Mr Sammler's Planet.
In 1976, he won the Pulitzer Prize for Humboldt's Gift. That same year Bellow was awarded the Nobel Prize, cited for his "human understanding and subtle analysis of contemporary culture".
In 2003, the Library of America issued a volume of Bellow's early novels, a rare tribute to a living writer for the non-profit publisher, which was created to preserve the US literary heritage.
"The backbone of 20th-century American literature has been provided by two novelists - William Faulkner and Saul Bellow," author Philip Roth said in a statement on Tuesday.
"Together they are the Melville, Hawthorne and Twain of the 20th century."
"If the soul is the mind at its purest, best, clearest, busiest, profoundest, then Bellow's charge has been to restore the soul to American literature"
Bellow's death leaves just one living US Nobel laureate in literature, Toni Morrison.
Bellow was the most acclaimed of a generation of Jewish writers who emerged after the second world war, among them Roth and Bernard Malamud.
To American letters, he brought the immigrant's hustle, the bookworm's brains and the high-minded notions of the born romantic.
"If the soul is the mind at its purest, best, clearest, busiest, profoundest," Cynthia Ozick wrote in 1984, "then Bellow's charge has been to restore the soul to American literature."
In spite, or perhaps because, of all the praise, Bellow also had detractors.
Norman Mailer called Augie March a "travelogue for timid intellectuals". Critic Alfred Kazin, a longtime friend who became estranged from Bellow, thought the author had become a "university intellectual" with "contempt for the lower orders".
Biographer James Atlas accused Bellow of favouring "subservient women in order to serve his own shaky self-image".
of 20th-century American literature
has been provided
by two novelists - William Faulkner and Saul Bellow"
Author Philip Roth
Old-fashioned, but not complacent, he kept writing into his 80s and, hoping to make his work more affordable, had his novella A Theft published as a paperback original in 1989.
His recent works included The Actual, a sentimental novella published in 1997, and Ravelstein, a 2000 novel based on the life of his late friend Allan Bloom, author of The Closing of the American Mind. Also in 2000, Bellow was the subject of Atlas' acclaimed biography.
He had five wives, three sons and, at age 84, a daughter.