Brogna attended Watertown High School in Watertown, Connecticut; where he played baseball, basketball and football. He was named to the All-State team as a quarterback and won the state championship in 1986. He was recruited as a quarterback by Clemson University, but chose to pursue a career in baseball. In 1999, he hit a career high 24 home runs for the Phillies. He also hit the first home run out of Coors Field. Brogna was diagnosed with ankylosing spondylitis, a form of spinal arthritis, in 1991, and had to take medication for the condition on a daily basis. Concerns surrounding his condition contributed to the decision of the Mets to trade him to the Phillies during the 1996 offseason, but he recovered sufficiently to be an offensive contributor for several seasons thereafter. He became national spokesperson for the Spondylitis Association of America.
Brogna retired in 2001.
In 2006 Brogna managed the Post University baseball team. The Eagles finished with a record of 13-40 overall and 6-19 in Central Atlantic Collegiate Conference play. He coached for the Nonnewaug Chiefs, a high school football team in Woodbury, Connecticut. He coached the Watertown High School boys basketball team from 2006 to 2009. Overall in Watertown, Connecticut, his win–loss record was 10–41. Soon after the conclusion of the 2008 football season, Brogna resigned as coach of the Chiefs and took a volunteer job as wide receivers coach for the Wesleyan University football team. In 2010 he managed the Mobile BayBears, the Arizona Diamondbacks Double-A minor league affiliate. In 2011 he was named the head football coach at Notre Dame-Fairfield high school in Connecticut, and stated he had retired from baseball (as a coach/executive) to concentrate his football duties year round. Brogna resigned as head coach in 2012 following a 1-9 record in his only season, and took a scouting job with the Tampa Bay Rays. In 2013, Rico Brogna returned to the Watertown High School gridiron as the special teams and defensive line coach. After the 2013 season Brogna was hired as special assistant to Jerry Dipoto, general manager of the Los Angeles Angels of Anaheim. In August 2014 Brogna was named the Angels player-information coach. He "felt a growth" during spring training in 2015, which was later diagnosed as testicular cancer. Five days after being notified of his condition, Brogna underwent surgery on May 13.
Brogna married Melissa Shuhart, whom he had met in high school, in 1992. They have two children, Alexa Grace and Hunter.