Carolina announced the news Tuesday.
The departures come one day after head coach Ron Rivera said he didn't expect anybody to leave his staff unless another organization hired them, per Brendan Marks of the Charlotte Observer.
Shula took over the Panthers offense in 2013 after two years as the team's quarterbacks coach. Along with four seasons as the head coach at the University of Alabama (2003-06), he spent nearly two decades as an offensive assistant with several NFL teams before arriving to Carolina.
"You got to go win, and sometimes even then you're going to get criticism. Our goal is to win every week and that's our No. 1 goal. You know that if you don't, there's going to be criticism, for good reason. That's what's great about sports, you have a bunch of fans watching the game and there's always opinions that come along with that – in any sport. You can't get caught up in that too much. Understand it, but my job is to stay locked in on getting points on the board."
Dorsey assumed the QBs coach role from Shula in 2013. He'd spent six seasons as an NFL signal-caller with the San Francisco 49ers—who selected him in the seventh round of the 2003 draft—and the Cleveland Browns.
The Panthers ranked 19th in total offense and 28th in passing yards per game during the 2017 season. Star quarterback Cam Newton had his second straight down year, throwing 22 touchdowns and 16 interceptions en route to a 80.7 passer rating, which ranked 24th in the league among qualified signal-callers.
Those are sharp declines from 2015, when Carolina was 11th in total offense and Newton finished tied for seventh in passer rating (99.4) during the regular season before the team advanced to Super Bowl 50, where it lost to the Denver Broncos.