Agganis’ family origins were from Longanikos near Sparta, Greece. Born in Lynn, Massachusetts from a large Greek family which includes four brothers and two sisters. He was a star football and baseball player at Lynn Classical High School as well as a strong student, being named as “All-Scholastic” from the state of Massachusetts. Aggainis enrolled at Boston University, where he became a starter, primarily at quarterback. After a sophomore season in 1949, when he set a school record by tossing fifteen touchdown passes, he entered the Marine Corps. Agganis played for the Camp Lejeune (N.C.) football and baseball teams. He received a dependency discharge from the Marines to support his mother and returned to college to play in 1951-52. Around the same time, Agganis was participating in summer baseball leagues in Augusta, Maine.  Agganis became the school’s first All-American in football and Boston coach Buff Donelli named Agganis the “greatest football player he ever coached”. He also played basketball and baseball in the school.

Agganis set another Boston University mark by passing for 1,402 yards (1,282 m) for the season and won the Bulger Lowe Award as New England’s outstanding football player. Coach Paul Brown of the Cleveland Browns thought he could be the successor to Otto Graham and drafted the college junior in the first round of the 1952 NFL Draft, offering him a bonus of $25,000. Boston Red Sox owner Tom Yawkey outbid Brown, however, and signed Agganis to play Major League Baseball for the Red Sox as a first baseman for $35,000. At the time of his death, Agganis was spending his off-season at his alma mater as an assistant coach, tutoring Tom Gastall, another quarterback who decided to play professional baseball and who died young.

Following his 1953 college graduation, Agganis played with the Triple-A Louisville where he hit .281 with 23 home runs and 108 RBI. He made his major league debut on April 13, 1954. Agganis had a modest rookie campaign, though he did lead American League first basemen in assists and fielding percentage. He hit 11 home runs that year, with 57 RBI and a .251 batting average.

In 1955, Agganis lost his starting position to rookie Norm Zauchin but regained his spot not long afterwards. On June 2, he was hospitalized with pneumonia after complaining of severe fever and chest pains. Though he rejoined the Red Sox ten days later and played two games against the Chicago White Sox, he fell ill again in Kansas City on June 27. He was diagnosed with a viral infection and was flown back to Sancta Maria Hospital in Cambridge, Massachusetts, where the doctor on duty stated that Agganis played too soon after his first illness, which probably was the reason for the second. The Red Sox placed him on the voluntary retired list until he recuperated, an early version of the disabled list. He began showing signs of improvement, before suffering a fatal pulmonary embolism on June 27, 1955. Baseball was in a state of shock upon hearing of Agganis death. Red Sox general manager Joe Cronin told the Associated Press that everyone related to the Red Sox organization was “grieved and shocked”, saying that Agganis was a “grand boy”, while stating that the team would be wearing for 30 black armbands to honor Agganis. American League president Will Harridge commented that his office was “saddened and shocked” by Agganis death, while Red Sox owner Tom Yawkey stated that he was “stunned” while calling Agganis a “man of great character”. Ten thousand mourners attended his wake, where his body was laid in state at St. George Greek Orthodox Church in Lynn.  Agganis was inducted into the College Football Hall of Fame in 1974. Gaffney Street, near the former site of Braves Field in Boston, was renamed Harry Agganis Way in his honor on November 11, 1995.