By the terms of the Treaty of Washington of 1897, Great Britain nominated Lord Herschell, the Chief Justice, and Lord Justice Richard Henn Collins, a Justice of the Court of Appeals and the Privy Council. They were at that period two of the leading judges in Great Britain. Venezuela, on the other hand, nominated Chief Justice of the Supreme Court of the United States, Melville Fuller, and another US Supreme Court Judge, David Brewer, who had served as Chairman of the dissolved United States Venezuelan Boundary Commission.

The choice of American judges by Venezuela was a sure indication of the full confidence that Venezuela held for the USA which championed its case throughout the period 1895-1899.

To choose the fifth arbitrator, the British and Venezuelan nominees were expected to submit to both Governments separate proposals of names of several jurists acceptable to each party. However, in both proposals, only the name of Frederic de Martens, a distinguished Russian writer on international law, appeared, and he was chosen as the fifth arbitrator and President of the Tribunal. Martens' scholarship, skill and integrity had become well known in international legal circles and, undoubtedly, these qualities influenced the judges chosen by Venezuela and Great Britain to name him as the President of the Tribunal. (In 1902, three years after the work of the Tribunal ended, de Martens was awarded the Nobel Peace Prize).

Just before the Tribunal was making arrangements to begin hearing of the case, Lord Herschell died and he was succeeded by the new British Chief Justice, Lord Charles Russell.

On the 15 March 1898 each party submitted its case in writing to the Tribunal. Venezuela's case was contained in three volumes and an atlas, while that of Great Britain was in seven volumes and an atlas. Four months later, on the 15 July 1898, each party submitted its rebuttal. Venezuela's rebuttal was presented in three volumes and an atlas while Great Britain's was in two volumes accompanied by six maps. Then on the 15 November 1898 each party submitted its final printed argument Venezuela's in two volumes and Great Britain's in one.

The hearing of the oral arguments was conducted in Paris, France, during a three-month period from 15 June to 15 September 1899. During this period there were fifty-four sessions of four hours each.

Great Britain was represented by a four-man counsel, namely, Sir Richard E. Webster, Attorney-General; Sir Robert T. Reid, a former Attorney-General; Mr. G. R. Askwith and Mr. Rowlatt.

Venezuela was also represented by four counsel, namely General Benjamin Harrison, a former President of the United States; Mr. Severo Mallet-Prevost, former Secretary of the United States Venezuelan Boundary Commission; General Benjamin T. Tracy, an ex-Defence Secretary of the United States; and James Russel Soley.

In opening Great Britain's oral arguments, Sir Richard Webster delivered a speech that lasted thirteen days. Mallet-Prevost, for Venezuela, followed this with one that also lasted thirteen days. After these two long arguments, Sir Richard Webster closed the case for Great Britain while General Harrison did so for Venezuela.

One week after the final oral session, the Tribunal on the 4 October 1899, presented a unanimous Award which put an end to the border controversy that had lasted for over fifty-eight years a controversy that nearly caused three countries (Great Britain and the United States of America and Venezuela) to go to war.

The Award, which was completed and signed by all five judges on the 3 October 1899, the day before it was handed down, stated: ". . .Now, we the undersigned Arbitrators do hereby make and publish our decision, determination, and Award of, upon and concerning the questions submitted to us by the said Treaty of Arbitration, and do hereby, conformably to the said Treaty of Arbitration, finally decide, award, and determine that the boundary-line between the Colony of British Guiana and the United States of Venezuela is as follows

Starting from the coast at Point Playa, the line of boundary shall run in a straight line to the River Barima at its junction with the River Mururuma, and thence along the mid-stream of the latter river to its source, and from that point to the junction of the River Haiowa with the Amakura, and thence along the mid-stream of the Amakura to its source in the Imataka Ridge, and thence in a south-westerly direction along the highest ridge of the spur of the Imataka Mountains to the highest point of the main range of such Imataka Mountains opposite to the source of the Barima, and thence along the main ridge in a south-easterly direction of the Imataka Mountains to the source of the Acarabisi, and thence along the mid-stream of the Acarabisi to the Cuyuni, and thence along the northern bank of the River Cuyuni westward to its junction with the Wenamu, and thence along the mid-stream of the Wenamu to its westernmost source, and thence in a direct line to the summit of Mount Roraima, and from Mount Roraima to the source of the Cotinga, and along the mid-stream of that river to its junction with the Takutu, and thence along the mid-stream of the Takutu to its source, and thence in a straight line to the westernmost point of the Akarai Mountains, and thence along the ridge of the Akarai Mountains to the source of the Corentin called the Cutara River. . ."