Morgan attended South Garland High School in Garland, Texas, and was a student and played football. In football, he was a three-year letterman. As a junior, he was named as an All-State selection by The Dallas Morning News. As a senior he was named the Team's Most Valuable Player, was an All-Area selection, All-Conference selection, All-State selection, and an All-America selection. Quincy Morgan graduated from South Garland High School in 1996.

Morgan spent two years at Blinn College in Brenham, Texas, before transferring to Kansas State University. In his two seasons, Morgan became one of only seven KSU players catch more than a hundred passes, and also one of only four players with more than 2,000 receiving yards. He was also the only Wildcat to notch 1,000 receiving yards in two consecutive seasons. Morgan ended his college experience as #6 on the all-time Wildcat receiving list.

He was a second-round draft pick of the Cleveland Browns in 2001, and played with the team until he was traded to Dallas midway through the 2004 season.

Morgan was traded to the Cowboys for Antonio Bryant, following a public dispute between Bryant and Cowboys head coach Bill Parcells. Morgan would have a rather mediocre season with the Cowboys in 2004, despite his rapid elevation on the depth chart following an injury to Terry Glenn. During the following offseason, Morgan performed poorly in an unexpected depth chart battle against Patrick Crayton and Parcells began to perceive him as uncompetitive. He was released in order for the Cowboys to pick up Peerless Price off waivers and was later signed by the Pittsburgh Steelers. During the 2005 regular season, Morgan recorded 9 receptions for 150 yards and 2 touchdowns. On September 3, 2006, Morgan was cut by the Steelers, along with 21 other players, as the team reached its final roster. Morgan then signed with the Broncos on September 18 as a backup wide receiver. On September 1, 2007 he was released by the Broncos.