The news comes one day after head coach Ron Rivera told reporters that he didn't expect any changes to the staff unless someone opts to take a job elsewhere.
Carolina's offense has failed to find its rhythm after leading the league in scoring in 2015. The Panthers finished 19th in total offense (323.7 yards per game) and 28th in passing (192.3) during the past regular season.
Shula spent seven seasons with the Panthers, working his first two in 2011-12 as the team's quarterbacks coach. He became Carolina's offensive coordinator in 2013.
The 52-year-old Shula joined the Panthers after four seasons as quarterbacks coach for the Jacksonville Jaguars from 2007-10. He was the head coach at the University of Alabama from 2003-06 after stops as an NFL assistant with the Tampa Bay Buccaneers (1988-90, 1996-99), Miami Dolphins (1991-92, 2000-02) and Chicago Bears (1993-95).
Dorsey has served as Carolina's quarterbacks coach from 2013-17 following two seasons as a pro scout for the team. The former University of Miami quarterback played six seasons in the NFL (2003-08) before finishing his playing career in the CFL in 2010.