The 20-year-old has signed a two-year contract with the Reds after the two clubs agreed an undisclosed fee for the striker.
Harry White (picture courtesy of www.gloucestercityafc.com)
Reds Head Coach Lee Johnson said, "We are pleased to welcome Harry on board. He is a player with good potential and I'm looking forward to keeping an eye on his progress under Paul Heckingbottom within our development squad.
"This is a fantastic place for young players like Harry as there is a genuine pathway into the first team."