White has agreed a two-year contract at Oakwell after scoring nine goals in 17 appearances for the National League North outfit, and Tykes boss Lee Johnson believes that the 20-year-old has the potential to establish himself at the Yorkshire side.
Johnson told the club's official website: "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."
The fee for White, who played college football in the United States before joining Gloucester, will remain undisclosed.