But a group formed by some of the king's distant relatives are considering whether to appeal against the decision. They want the king re-interred at York Minster.
Richard's battle-scarred bones were found under a council car park in Leicester in 2012. Centuries earlier, in August 1485, he had become the last English king to die in battle.
Three judges rejected an attempt by the Plantagenet Alliance, acting on behalf of the monarch's "collateral descendants", to force Justice Secretary Chris Grayling to set up a wide-ranging public consultation exercise to decide where his final resting place should be.
The judges ruled there were no legal reasons why plans to re-bury him at Leicester Cathedral should not go ahead.
The costly legal challenge has led to angry condemnation of the Alliance by Mr Grayling, but the group says it raised an issue of legitimate public interest.
It is understood that, by mid-March, the Government had run up costs of £82,000 on the legal battle.
There was applause at Leicester Cathedral as Bishop of Leicester Tim Stevens read out the High Court decision in London at 10am to a crowd of supporters and media.
The lawyer who spearheaded the alliance's legal challenge described the court's verdict as "highly regrettable".
Matthew Howarth, partner at Yorkshire law firm Gordons, said an appeal was now under consideration.
The Alliance claimed the exhumation licence granted by the Justice Secretary in September 2012 to the University of Leicester was legally flawed because he had not attached conditions ordering consultations on re-interment.
Richard was killed at the Battle of Bosworth in 1485 - ending the Wars of the Roses and the Plantagenet dynasty.