Born and raised in Baltimore, Maryland, Fugett attended Cardinal Gibbons School, where he started playing football as a senior, becoming a two-way player (tight end and defensive end). He graduated in 1968 and was named the Baltimore Catholic Athlete of the Year, the first black athlete to be given the award.
He accepted a scholarship to Amherst College in Massachusetts, because he wanted to go to a school where he could play both basketball and football. He received Little All-American honors in 1971.
Fugett was selected in the thirteenth round of the 1972 NFL Draft by the Super Bowl champion Dallas Cowboys. The Cowboys carried only two tight ends on the roster in those years, but saw potential in the 20-year-old rookie and made an exception by adding him as the third one. The next year, Billy Joe DuPree was taken in the first round of the 1973 NFL Draft and became an instant starter at tight end.
In 1975, Fugett started nine games and was the team's second leading receiver (behind Drew Pearson), with 38 receptions for 488 yards and three touchdowns. He also started Super Bowl X against the Pittsburgh Steelers.
After the courts ruled in favor of the National Football League Players Association, a new form of free agency was briefly instituted in 1976. Fugett signed as a free agent with the Washington Redskins and was looked upon as the replacement of former All-Pro Jerry Smith.
In 1977, he registered 36 receptions for 631 yards and five touchdowns. At the end of the year, he was tied with the St. Louis Cardinals' J. V. Cain in Pro Bowl votes, but edged him based on the team records.
In 1979, he was limited with a knee injury and was replaced in the starting lineup with rookie Don Warren. He retired prior to the 1980 season, after he did not receive a contract offer from the Redskins.
During his time with the Redskins, Fugett earned his law degree at the George Washington University Law School, attending school only at night. After his eighth year as an all pro tight end in the NFL and passing the Maryland state bar exam, he made the decision of joining his older brother Reginald Lewis in business.
While working with Lewis Fugett largely contributed the founding of TLC Group in 1983. From there he served as Director and Vice-Chair of the McCall Pattern Company Management Committee, as founding partner of a Baltimore law firm, and as a partner with Fanfone in Europe. After the death of his brother in 1993, Fugett took over TLC Beatrice International Foods, the largest black-owned and black managed business in the United States at the time. At its peak, TLC Beatrice had $2.2 billion in sales and was number 512 on Fortune magazine’s list of 1,000 largest.
In addition to his law practice, Fugett is the most recent past President of the Retired Players Steering Committee of the National Football League Players Association, as legal counsel and advisor to Wall Street investment services firm GFS Acquisition Partners, Managing Director of Axum Capital Partners, and on the Leadership Council for the American Diabetes Association Maryland Chapter. Fugett is currently working on his memoirs to be published in the near future.
Fugett currently resides in Baltimore with his wife Carlotta. His two sons are Joseph "Russell" and Reginald. His only daughter Audie married Adam Jones in late-December 2014.