Buoniconti was born to Nicholas Anthony Buoniconti Sr. and Pasqualina "Patsy" Mercolino in Springfield, Massachusetts. The couple ran a family bakery in the predominantly Italian South End of the city. He was raised Catholic and played football for Cathedral High School, where a plaque honoring him as a "Hometown Hall of Famer" was unveiled in 2012.
In 1960, As a junior, was second on the Fighting Irish in tackles (behind senior captain Myron Pottios) with 71. As a senior in 1961 led the team with 74 tackles as the Irish co-captain and was rewarded with 2nd-team All-America selections from UPI, TSN, and the Football Coaches' Association. He was the only All-American on Notre Dame's 1961 team.
As a tackle, Buoniconti was the captain of the 1961 Notre Dame football team, but was considered by NFL scouts as "too small" to play pro football. Drafted by the Boston Patriots in the 1962 American Football League college draft and switched to linebacker, Buoniconti made an immediate impact, as he was named the team's rookie of the year. The following year, he helped Boston capture the 1963 AFL Eastern Division title. With Boston, he appeared in five AFL All-Star Games, and recorded 24 interceptions, which is still the seventh-most in team history. He was named 2nd team All-AFL in 1963 and the following season began a run of five consensus All-AFL seasons in the following six seasons, missing only 1968 when he was named second-team All-AFL. Buoniconti is a member of the Patriots All-1960s (AFL) Team and the AFL All-Time Team.
His leadership made him a cornerstone of the Dolphins' defense. During his years there, the team advanced to three consecutive Super Bowl appearances, the second of which was the team's 1972 undefeated season. In 1973, he recorded a then-team record 162 tackles (91 unassisted). He was named to the AFC-NFC Pro Bowl in 1972 and 1973.
Buoniconti ended his career with an unofficial 24 sacks, eighteen with the Patriots and six while with the Dolphins.
He was named the Dolphins' Most Valuable Player three times (1969, 1970, 1973). In 1990, he was voted as a linebacker on the Dolphins' Silver Anniversary All-Time team. On November 18, 1991, he was enshrined on the Miami Dolphin's Honor Roll at Joe Robbie Stadium.
Buoniconti earned his law degree during his years with the Patriots. He was a practicing attorney for a short time. He was also president of the US Tobacco Company during the late 1970s and early 1980s. Buoniconti was a leading critic of studies which showed that smokeless tobacco caused cancer of the mouth as well as other types of cancer.
In recent years, he has become the most outspoken member of the 1972 team; it is rumored that he leads a champagne toast every year after the last remaining undefeated team loses for the first time. Also, it is reported that Buoniconti sends a Christmas card every year to former Minnesota Vikings defensive end Bob Lurtsema, whose roughing-the-passer violation in an early 1972 game aided the Dolphins' undefeated season.
Buoniconti also appeared in one of the Miller Lite "Do you know me?" TV ads, in which he talked about the No-Name Defense. The punch line was a variation on an old joke, with Buoniconti remarking that everyone knows him now. A passerby remarks, "Hey, I know you... you're... uh... uh..." trying to recall Buoniconti's name. Upon being told that it's Nick Buoniconti, the passerby says, "No, that's not it."
Buoniconti put his verbal talent to use as a co-host of the HBO series Inside the NFL until 2001. That same year, Buoniconti was named to the Pro Football Hall of Fame.
Buoniconti is a member of the National Italian American Sports Hall of Fame.