Garment, who had been ill, died Saturday at his Manhattan home, his wife, Suzanne Garment, said today.
Garment and Nixon met when Nixon joined the law firm where Garment was a partner in 1963.
The two men became close, and Garment went to work in the Nixon White House, serving on a number of projects and becoming White House counsel.
The Watergate scandal developed from a break-in at Democratic National Committee offices at the Watergate complex in Washington, DC, in 1972, and the Nixon administration's subsequent efforts to cover up its involvement in it.
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The conversations involved Nixon and various officials and staff members in the White House.
When the Watergate scandal broke and the system came to light, prosecutors demanded the tapes to know what Nixon had said.
The tapes played a major role in the erosion of Nixon's public support and led to his resignation as Congress considered impeachment.
Garment left the White House in 1973 before Nixon's resignation and became a high-profile Washington lawyer. His clients included televangelist Oral Roberts and financier Marc Rich.
An avid musician, he played the clarinet and the saxophone and even performed in musical gigs in various bands. That love of music would follow him throughout his life, and he was among the founders of the National Jazz Museum in Harlem. He later served as its chairman.
Besides his wife, he is survived by his daughter, Dr Ann Garment, and his brother, Martin Garment.
Garment's first wife died in 1977. Another daughter died in 2011, and his son died in 2012.