The 20-year-old rejected a new contract at United and joined Burnley on a four-year deal last summer.
The two clubs failed to agree a fee at the time but the Football Association tribunal has resolved the dispute.
Burnley chief executive Paul Fletcher said: “The outcome is satisfactory.
“When the smallest club in the league tries to take on the biggest club you always wonder how it’s going to end up.
“But we thank the tribunal for taking a common sense approach to this.
“We have always valued the player around the £300,000 mark until he starts establishing himself in the first team.”
Fletcher added: “When United were asking a million-plus we thought we had to stand up and be counted — and that’s what we did.”