Carmichael played quarterback on the high school football team at William M. Raines High School in Jacksonville, Florida.
He played college football at Southern University, where he moved to wide receiver. He also played on the basketball team as a center and threw the javelin and discus for the track and field team. He was drafted by the Eagles in the 7th round of the 1971 NFL Draft.
Early in his career, Carmichael showed his significant physical tools but struggled with injuries and being moved between the tight end and wide receiver positions before eventually finding his place as a wide receiver.
He was elected to four Pro Bowls in his NFL career, and led the league in receptions and receiving yards during the 1973 season. He finished third in receiving yards in 1978 with 1,072 and was second in receiving touchdowns in 1979 with 11.
In 1980, he set an NFL record at the time by catching passes in 127 consecutive NFL games. He was also the Eagles' top receiver of Super Bowl XV, with six catches for 91 yards.
In 1984, he was cut by the Eagles and then by the New York Jets before signing with the Dallas Cowboys. He caught only one pass that season before being cut by the Cowboys and retiring.
He ended his career with 590 receptions for 8,985 yards with 79 career touchdown catches, along with 64 rushing yards on nine carries. He currently ranks 18th all-time in career touchdown receptions. At 6 foot 8 inches, he is believed to be the tallest wide receiver in the history of the NFL.
After retiring from his playing career, he settled in South Jersey and joined a Philadelphia travel agency as a vice president for sales. He later operated various businesses, including in steel fabrication and sports marketing.
In 1998, Carmichael was named the director of player and community relations for the Eagles, a newly created position where he would be a "combination mentor, confidant, troubleshooter, and liaison between the players and the authority figures in the organization". He was moved to a Fan Engagement Liaison position in 2014, and retired from that role on April 2, 2015. He currently works as an ambassador for the team in his retirement.