The 19-year-old winger has spent time on loan in the third tier for the last two seasons, winning promotion both times with Barnsley and Sheffield United, and was also part of the England side that won the Under-20 World Cup in South Korea in June.
"It's a massive club," Chapman said of Rovers, who were relegated from the Championship last season.
"They shouldn't be in this league, they need to get back to where they belong, up the top, and I'm here to help out and I can't wait to get started.
"It would be unbelievable if I can do three out of three and with the squad we've got here I don't see why we can't."
Chapman becomes Tony Mowbray's eighth signing of the summer and goes straight into the squad for this weekend's season opener at Southend United.