Rovers have added to their forward options by beating other clubs to the signature of the 22-year-old, who joins on a four-year deal from Leicester City.
"It is another good signing for us, Ben fits into the model of what we are trying to achieve here," said the Rovers boss.
"He is a good technician, he's a good age, and he has his best football ahead of him.
"He can create and score goals and I've been impressed with his desire to join the football club.
"He obviously impressed in the two games against us last year, and he's been schooled in the right way at Manchester United and Crewe Alexandra.
"Several other clubs were interested him, so I am grateful to the owners in backing us because we are convinced he'll be a fans favourite.
subscribers can see our exclusive interview with Marshall online right now. Sign up today from just 10p a day!