Rovers boss McSheffrey was critical of the culture he inherited after taking over from Richie Wellens in early December.
The 39-year-old suggested standards had slipped and claimed the fitness level of the squad was simply not up to scratch.
But with the help of Coppinger – whose job will involve nailing down the club’s identity and culture – McSheffrey is confident that improvements already made in those areas will continue.
“He’s been a legend at the club and he’s stepped onto the other side now,” said McSheffrey.
“He’s been studying the role, visiting a lot of clubs and seeing how they do things in that head of football operations-type role.
“I’m delighted to have him on board.
“He’s good support for me and he’s got high standards. You don’t play as long as he did if you’re sloppy with things.
“Between us we really want to get the standards of the club really high.”
McSheffrey and Coppinger will form part of new-look recruitment team following this weeks’ departure of Graham Younger, the club’s head of talent identification.
Rovers, whose relegation to League Two will be confirmed this weekend, have revealed that a successor to Younger will be sought.
On whether recruitment has started for next season, McSheffrey said: "Phone calls are already being made and conversations are being had.
"We need to be on the front foot with it but at times be patient with it to get the right ones.
"Amongst all the disappointment, it’s an exciting summer.”