The 23-year-old, who scored 12 goals in 41 appearances while on loan at Walsall in League Two last season, was confirmed as Rovers’ second signing of the summer on Monday.
Miller has penned a three-year deal at the Eco-Power Stadium.
“We’re delighted to get him over the line,” said McSheffrey, whose side has now returned to pre-season training.
“There was competition, there were plenty of clubs interested in him.
“For him to choose us after the initial meeting is really good and shows we’re doing things right.”
The deal had been in the pipeline for ‘a couple of weeks’, Miller said.
He came onto the club’s radar after McSheffrey and head of football operations James Coppinger took an unusual approach to scouting prospective strikers.
The Rovers chief said: “We did this one a little bit different. We gave a scout a player profile for what we wanted in a striker and what we felt that we were missing with the types of qualities he needs.
“George was one of the few names that came back. We really studied it, narrowed it down to a couple, and we felt George was the one for us.”
McSheffrey wanted to add energy to his front line.
He said: “It was no secret that we needed legs and willing runners, energy that can last 90 minutes.
“Chasing lost causes is one of the non-negotiables I love in a footballer.
"Fans love it. They love to see their strikers chasing and pressing from the front is the modern game now.”