Accorsi's tenure with the Colts was short-lived, as the team moved to Indianapolis in 1984. He then joined the Cleveland Browns as their general manager in 1985. During his time with the Browns, Accorsi helped build a team that made the playoffs five times in six years, including three trips to the AFC Championship Game.
In 1992, Accorsi left the Browns to become the general manager of the New York Giants. He quickly made his mark on the team, drafting quarterback Dave Brown and running back Tyrone Wheatley in his first year on the job. Accorsi also made a bold move in 2004, trading for quarterback Eli Manning on draft day. Manning went on to lead the Giants to two Super Bowl victories during his career with the team.
Accorsi retired from his position with the Giants in 2006, but he continued to be involved in the NFL in various capacities. He served on the league's competition committee and was a consultant for several teams, including the Carolina Panthers and the Detroit Lions.
Throughout his career, Accorsi was known for his keen eye for talent and his ability to build successful teams. He was inducted into the Giants' Ring of Honor in 2016, and he remains a respected figure in the NFL community.