Eckersley joined the Clarets last summer on a four-year deal after rejecting a new contract at Old Trafford, but the two clubs failed to reach an agreement on the value of the 20-year-old.
United were hoping for over £1million for their former trainee - who is yet to start a game in the Barclays Premier League - but Burnley's valuation was significantly lower.
"The outcome is satisfactory," Burnley chief executive Paul Fletcher told the club's official website.
"When the smallest club in the league tries to take on the biggest club in the league 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."