Born in Ansonia, Connecticut, Skoronski went to high school at Fairfield College Preparatory School in Connecticut, and played college football at Indiana University in Bloomington. As a senior in 1955, he was the Hoosiers" most valuable player and averaged fifty minutes per game. Skoronski was selected in the fifth round of the 1956 NFL draft, 56th overall, by the Green Bay Packers.
He started at left tackle in his rookie season in 1956 under third-year head coach Lisle Blackbourn, and then served two years in the United States. Air Force.
Skoronski returned to the team in 1959, the first season under head coach Vince Lombardi. Skoronski was the left tackle and offensive captain on Lombardi"s five NFL championship teams.
He played in the Pro Bowl following the 1966 season (and the first Super Bowl). Following his eleventh season in the NFL, Skoronski retired in June 1969, and was elected to the Packers Hall of Fame in 1976.