As Commissioner of the Dutch East Indies he instituted the landrente tax system in the Dutch East Indies in 1816, and in 1819 promulgated the new Regeringsreglement for that colony together with his colleagues Godert van der Capellen and Arnold Adriaan Buyskes, while also reforming the coinage.

He completed his legal studies at Leiden University.He defended his dissertation, entitled De testamento duorum una tabula condito[a] on 21 June 1788.

[b] In 1804 he was, with CA Ver Huell and JW Janssens, nominated by the Asiatic Council[c] as Governor-General of the Netherlands Indies.

After the Annexation to the First French Empire in 1810, he was first appointed in a conseil pour les affaires de la Hollande to help with the transition,[4] but later withdrew from all employment and in 1811 established his residence in The Hague, where he came into close contact with the members of the Triumvirate of 1813.

In both positions, he rendered excellent services,[d] enjoyed the confidence of the Belgians, including the Count de Merode, and showed himself averse to centralization and all-out involvement of the state in religion, education, science, trade and industry, and committed to true freedom.

Specifically, he zealously advocated freedom of the press, public deliberation of the States General, and exclusion of all monopoly in overseas possessions.

On the recommendation of Caspar Georg Carl Reinwardt, the director of the department of Agriculture, the system of primary education was reformed, giving a foundation for the efforts in the 19th century to combat illiteracy in the colony.

The ship foundered, and though the passengers and crew were rescued, Elout lost his personal belongings, among which his diaries in which he had noted all details of his work in the Indies.

He was also a member of the Society of Dutch Literature in Leiden and Director of the Hollandsche Maatschappij van Wetenschappen in Haarlem.