Bradlee, who was 93, died of natural causes on Tuesday at his Washington home.
US President Barack Obama, in his tribute, called him a "true newspaperman".
"For Benjamin Bradlee, journalism was more than a profession -- it was a public good vital to our democracy," Obama said.
"A true newspaperman, he transformed the Washington Post into one of the country's finest newspapers, and with him at the helm, a growing army of reporters published the Pentagon Papers, exposed Watergate, and told stories that needed to be told -- stories that helped us understand our world and one another a little bit better," he said.
The standard he set -- a standard for honest, objective, meticulous reporting -- encouraged so many others to enter the profession, Obama said.
"And that standard is why, last November, I was proud to honour Ben with the Presidential Medal of Freedom. Today, we offer our thoughts and prayers to Ben's family, and all who were fortunate to share in what truly was a good life," said the US President.
"From the moment he took over the Post newsroom in 1965, Mr Bradlee sought to create an important newspaper that would go far beyond the traditional model of a metropolitan daily," the Post said.
"He achieved that goal by combining compelling news stories based on aggressive reporting with engaging feature pieces of a kind previously associated with the best magazines.
"His charm and gift for leadership helped him hire and inspire a talented staff and eventually made him the most celebrated newspaper editor of his era," the daily said.
"The most compelling story of Bradlee's tenure, almost certainly the one of greatest consequence, was Watergate, a political scandal touched off by the Post's reporting that ended in the only resignation of a president in US history," the Post reported.
"He had the touch," said Watergate reporter Bob Woodward. "He had the ability to encourage people, stimulate people but not run over people.”
Woodward said Bradlee was "truly a great editor, probably the greatest editor of the 20th century."
"He created an atmosphere in the newsroom of the Washington Post that spelt... ‘There are mysteries out there. There are things we don't know about. We're not getting to the bottom of it. Human behaviour is hidden from us and so we have to keep digging at it’," Woodward said.
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