It is currently unclear whether or not the Alliance will seek to appeal. Any further matters stemming from the judgment will be dealt with at a later date.
Mr Grayling angrily condemned the Alliance legal action, saying it had "taken up so much time and money".
Mr Grayling said: "I have been very clear from the start that the decision to grant an exhumation licence for Richard III was taken correctly and in line with the law.
"I am pleased the court has reached the same conclusion and comprehensively rejected all of the claimant's arguments.
"I am, however, frustrated and angry that the Plantagenet Alliance - a group with tenuous claims to being relatives of Richard III - have taken up so much time and public money.
"This case, brought by a shell company set up by the Alliance to avoid paying legal costs, is an example of exactly why the Government is bringing forward a package of reforms to the judicial review process."
Distant relatives of King Richard III have lost their High Court battle over where the monarch's remains should be reburied.Read the full story ›
Today three judges ruled that is where they should remain and it was "time for King Richard III to be given a dignified reburial, and finally laid to rest".
The judges rejected a bid by relatives who make up the Plantagenet Alliance for a ruling that Mr Grayling is under a legal duty to set up a wide-ranging public consultation exercise to decide where the king's final resting place should be.
Distant relatives of King Richard III have lost their High Court battle with Justice Secretary Chris Grayling over where the monarch's recently-discovered remains should be reburied.
The King's bones are likely to now be buried in Leicester, not York as they had hoped.
Fresh doubt has been raised over the bones of Richard the Third.
Two leading academics have called for a coroner's style inquiry as they claim the bones could be those of any of the King's descendants.
They say the DNA evidence is not enough to be able to say for sure. Leicester University, who found the bones, say they're still confident it's him.
Distant relatives of King Richard III will have to wait to learn whether they have won their High Court battle with Justice Secretary Chris Grayling over where the monarch's recently-discovered remains should be reburied.
In an unprecedented legal battle, relatives who make up the Plantagenet Alliance asked three judges to rule that Mr Grayling is under a legal duty to set up a wide-ranging public consultation exercise to decide the question.
Their counsel Gerard Clarke argued the Queen and royal household should be at the top of the list of consultees, and it should include the distant relatives themselves as well as general members of the public.
Mr Clarke said the issue was important as the last English king to die in battle "is not just any old bones".
Government QC James Eadie told the court Mr Grayling was "under no statutory or common law duty to consult".
Lady Justice Hallett, sitting with Mr Justice Ouseley and Mr Justice Haddon-Cave, said the court would take time to consider its judgment and told the parties: "We shall let you know our decision as soon as possible."
Richard's battle-scarred bones were discovered under a council car park in Leicester and the current plan is for them to be reinterred at the city's cathedral.
Richard was killed at the Battle of Bosworth in 1485 - ending the Wars of the Roses and the Plantagenet dynasty - and his body was taken to Leicester by supporters of the victorious Henry VII and buried in Greyfriars church, now the site of the council car park.
The Plantagenet Alliance want the remains to be buried at York Minster, claiming that was the wish "of the last medieval king of England", who was known as Richard of York.
Mr Clarke said in a two-day hearing the alliance would be satisfied with a wide-ranging public consultation exercise on where the king's final resting place should be.
A Leicester City Council representative has told the High Court that the council has no commonlaw duty to consult about where to reinter the remains of Richard III.
He had added the council was "more than happy" with the university's burial plans, and said it was time to let his remains be reburied in what he called "the beautiful surroundings of Leicester Cathedral".
Judges at the High Court in London are due to rule today on where the remains of Richard III will be buried.
Campaigners from York, who want them brought to the city, sought a judicial review to overturn a decision for the remains to be laid to rest in Leicester.
Descendants of Richard III are calling for a public consultation to determine where his remains should be buried.
The relatives of the monarch are asking judges at the High Court in London to rule that Justice Secretary Chris Grayling is under a legal duty to allow a consultation.
Richard III’s battle-scarred bones were discovered under a council car park in Leicester and the current plan is for them to be reinterred at the city's cathedral.
The Plantagenet Alliance Ltd, formed by the distant relatives, want the remains to be buried at York Minster. They claim that is what Richard III, who was from the House of York, would have wanted.
The Plantagenet Alliance Ltd, formed by the distant relatives of King Richard III, are fighting for the late monarch's remains to be buried at York Minster, claiming it was the king's wish.
They are bringing judicial review proceedings against Justice Secretary Chris Grayling, the University of Leicester - which intends to bury the remains at Leicester Cathedral - and Leicester City Council.
Their solicitor, Matthew Howarth, from law firm Gordons, said:
Quite why our opponents have declined the obviously sensible option of independent adjudication, preferring to incur substantial legal costs - including for the taxpayer - and tie up considerable court time, is inexplicable.
Although many people are astonished we've got this far, we'll go to the hearing with every confidence in our position, intending to state our case clearly and believing there's every chance the licence will be quashed.
If that happens, the odds about the king eventually being laid to rest in York will shorten dramatically.
At the heart of the case is a Ministry of Justice decision to grant a "section 25 licence" under the Burial Act giving archaeologists from the university licence to excavate, and the university permission to decide where to re-bury the bones, which were exhumed in the city 19 months ago.