The International Equestrian Federation (FEI) also suspended the 32-year-old Lynch from competing in the sport for three months.

The ban runs out November 21 after taking effect from the day Lynch was provisionally suspended from the Games.

His horse Lantinus tested positive for capsaicin, a banned pain relieving medication derived from chili peppers.

Lynch and Lantinus finished tied for seventh in qualifying in the individual jumping class but were prevented from taking part in the final, which was held in Hong Kong.

The world governing body ordered him to pay 3,750 Swiss francs (£1,908) as a fine and legal costs.

Lynch has 30 days to appeal the verdict at the Court of Arbitration for Sport but he said that he will not be challenging it.

He said: "With the FEI taking nearly two months to announce its decision, there seems little point me now appealing it.

"I just want to get back in the ring and I feel the best way that I can thank my family, friends and my owner, Thomas Fruhmann, for their support over the past number of weeks is to start winning again.

"Before I do, however, I will go back home to thank people personally."

It is the second consecutive Olympics that an Irish show jumper has been disqualified and banned.

In Athens four years ago Cian O'Connor was stripped of the gold medal after his horse Waterford Crystal tested positive.

Joe Walsh, the chairman of Horse Sport Ireland, said that the group would study the FEI ruling to ensure it never happened again.

He said: "I want to assure people that we will be relentless in dealing with this issue."

Five horses failed dope tests at the Games.

As well as Lynch's ride, they were Chupa Chup, ridden by Brazil's Bernardo Alves, Coster, the mount of Christian Ahlmann of Germany, Camiro, under Norway's Tony Andre Hansen, and Rufus, ridden by Brazil's Rodrigo Pessoa.

Pessoa, promoted to the 2004 Olympic gold medal after O'Connor was disqualified, had already been banned for four-and-a-half months.

He had successfully challenged that suspsension in a civil court in Brazil but was warned by the FEI he faced further sanctions if he competed in the Global Champions Tour Final in Sao Paolo this weekend.

Alexander McLin, the FEI's secretary general, said: “We understand that he has obtained an injunction from a national court compelling the Brazilian National Federation to enter him in the event.

"That he should take such action is highly disappointing and inappropriate for a sportsman in his position. 

"We will take all necessary further disciplinary action should local court orders or circumstances allow him to take part in the competition. 

"Any result obtained by him in an international competition while under suspension would be void.”

 Contact the writer of this story at [email protected]