Campo attended Robert E. Fitch High School in Groton, Connecticut, where he lettered in football and baseball.
Campo attended Central Connecticut State, where he lettered football and baseball. In football, he played defensive back. In baseball, he played shortstop and was a two-time All-East selection. In 1999, Campo was awarded an honorary doctoral degree from his alma mater. Of more than 50 such degrees awarded by CCSU, Campo's remains the only one titled Doctor of Health and Physical Education.
Campo began his coaching career in 1971 at his alma mater, coaching two seasons followed by stints at Albany (1973); Bridgeport (1974); Pitt (1975); Washington State (1976); Boise State (1977–79); Oregon State (1980); Weber State (1981–82); Iowa State (1983); and Syracuse (1984–86).
In 1987, Campo joined the University of Miami staff under head coach Jimmy Johnson as secondary coach. At Miami, he helped the Hurricanes to a two-year record of 23–1 and the 1987 National Championship. Safety Bennie Blades was the 1987 Thorpe Award winner before being selected with the third pick in the NFL draft by the Detroit Lions.
After two seasons with the Hurricanes, Campo followed Johnson to the Dallas Cowboys in 1989 as a defensive assistant coach. After Dick Nolan (a Landry holdover) left following the 1990 season, Campo became the defensive backs coach and was a part of two Super Bowl championships (the 1992 and 1993 seasons). When Butch Davis left the Cowboys to become the Miami Hurricanes' head coach after the 1994 season, Campo was promoted to defensive coordinator. In his first season as defensive coordinator, the Cowboys won the Super Bowl. After five seasons as defensive coordinator, Campo was named as the fifth head coach of the Cowboys on January 26, 2000.
After the firing of Chan Gailey in 2000, he was hired to take over the head coaching duties of the Dallas Cowboys, over candidates Joe Avezzano and Hudson Houck.
Campo's head coaching debut was marred by a successfully executed, surprise on-side kick on the opening kickoff by the underdog Philadelphia Eagles in the season opener. Later in the game, the Cowboys lost Joey Galloway, their prize off-season free agent acquisition, for the season and quarterback Troy Aikman for several games with a concussion. The Cowboys lost to the Eagles 41–14 and ultimately finished the season at 5–11.
With considerably lower expectations for the 2001 season after Aikman's retirement, the Cowboys again finished 5–11, but Campo was given credit by many for getting the most out of a less talented team. However, Campo was harshly criticized after a Thanksgiving Day game against the Denver Broncos when, trailing 26–10 early in the fourth quarter, Dallas scored a touchdown to make the score 26–16. Campo at first decided to go for two which would narrow the lead to 8 points (a one possession game) but after a timeout decided to kick the extra point leaving Dallas down by 9 points and needing two possessions rather than one. Dallas was only able to score one more touchdown and lost 26–24.
In 2002, Dallas was believed to have much better talent, having acquired all pro defensive lineman La'Roi Glover and drafting talents such as safety Roy Williams and receiver Antonio Bryant, and a now-more experienced starting quarterback in Quincy Carter. The team was featured on HBO's Hard Knocks in the pre-season and Campo's leadership on that show was widely praised. However, the Cowboys stumbled in the season opener losing to the expansion Houston Texans in the Texans' very first game. Dallas entered week 13 with a 5–7 record and led the San Francisco 49ers 27–24 with about 2 minutes to play. Facing a fourth and one at the 30-yard line, Campo opted for a field goal attempt even though there was a considerable amount of time left in the game. The attempt failed and taking over at the 30, the 49ers drove down the field to win the game. Campo's team was blown out the next two games and finished the season 5-11 again, after which he was fired. To date, he is the only Cowboys head coach to have left the team without posting a winning season or coaching a playoff game.
After his dismissal from the Cowboys, Campo was hired as defensive coordinator by Cleveland Browns head coach Butch Davis, Campo's predecessor as Cowboys defensive coordinator. After Davis resigned from the Browns, his successor Romeo Crennel, fired Campo. Campo then joined the Jacksonville Jaguars as assistant head coach and secondary coach. In January 2008, Campo was re-hired by the Cowboys as their secondary coach.
On January 13, 2012, Kansas head coach Charlie Weis hired Campo as defensive coordinator and defensive backs coach.