Bradlee led the newspaper for 26 years starting in 1965.
The Watergate story started when two then-young Post reporters, Bob Woodward and Carl Bernstein, spent months pursuing an election-year break-in attempt at the opposition Democratic Party headquarters in which a crew of politically linked burglars were arrested.
The investigation found links to Nixon's campaign organisation and eventually led to congressional hearings that exposed broader corruption.
Nixon resigned in 1974 with the House of Representatives poised to vote for his impeachment.
Woodward and Bernstein subsequently won the Pulitzer Prize, the most prestigious award in US journalism.
"For Benjamin Bradlee, journalism was more than a profession - it was a public good vital to our democracy," said President Barack Obama.
"A true newspaperman, he transformed the Washington Post into one of the country's finest newspapers," he said in a statement.