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Giving the judgement to a packed and hushed courtroom, Chief Justice Warren E. Burger said the court rejected Mr Nixon's claims of executive privilege.
Instead, he said they "must yield to the demonstrated, specific need for evidence in a pending criminal trial".
The president said he was "disappointed" by the decision, but would comply with the ruling.
The White House has already released edited transcripts of the tapes, which cover 64 conversations made between June 1972 and April of this year.
But President Nixon has until now refused to comply with a court order awarded to Leon Jaworski, the special prosecutor in the Watergate investigation, requiring him to produce the tapes themselves.
Mr Jaworski alleges the tapes implicate the president himself in covering up a break-in at the Watergate hotel headquarters of the Democratic National Committee during the election campaign in 1972.
The burglars were caught rifling through confidential papers and bugging the office of President Nixon's political opponents.
The tapes will now be available for use as evidence in the trial of some of the president's closest aides, due to take place in September.
It is likely to take several weeks to produce transcripts of the tapes, so they will not be available in time to be used during the House of Representatives' Judiciary Committee debate on impeachment, which began this evening.
However, the timing of the Supreme Court decision just hours before the debate began, as well as the fact that all eight judges voted unanimously, is likely to have a strong influence on the impeachment process.
If the committee decides to recommend impeaching the president, the matter goes to the full House for debate.
If the House agrees, President Nixon could face an impeachment trial before the Senate - the first such trial in over a century.
When the tapes were finally released, more than 18 minutes of a crucial meeting were found to be missing.
The official explanation was that the president's secretary had accidentally erased it by pressing the wrong foot-pedal while answering the phone.
On 27 July, the House Judiciary Committee voted to recommend that the president be impeached and removed from office.
But before the House debate on his impeachment could begin, President Nixon resigned.
Richard Nixon's successor, Gerald Ford, formally pardoned him just two months after coming into power, saving him from possible prosecution.
But the five Watergate burglars and two co-plotters, former White House staff member G. Gordon Liddy and Howard Hunt, were jailed.
In total 40 government officials were either indicted or jailed.
Nixon eventually re-established himself as a respected statesman. He died in 1994.
In June 2005, former FBI deputy head Mark Felt was revealed to be the anonymous source "Deep Throat", who helped Washington Post reporters Bob Woodward and Carl Bernstein uncover the Watergate affair.
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