He was born in Newton Abbot, England, the son of a solicitor. He attended Westminster School until 1866, when the family emigrated to Australia following his father's bankruptcy, settling in Rockhampton, Queensland. D'Arcy continued his studies and chose to follow law, later joining his father's business. He did well and began to speculate, initially in land. He married Elena Birkbeck of Rockhampton at St Patrick's Cathedral, Parramatta on 23 October 1872. Elena was born in Mexico in 1840, the only daughter of Damiana de Barre Valdez and Samuel Birkbeck, a mining engineer from Illinois in the United States, who was in Mexico managing a silver mine. He was descended from the English Birkbecks, a Quaker family with an interest in education.
In 1882 he became a partner, with Walter Russell Hall and Thomas Skarratt Hall, in a syndicate with Thomas, Frederick and Edwin Morgan when they opened a mine on Ironstone Mountain, in Queensland, south of Rockhampton. There was a significant deposit at Mount Morgan Mine. In October 1886, the syndicate became the Mount Morgan Gold Mining Company, with D'Arcy a director and the largest shareholder. He held 125,000 shares in his own name and 233,000 in trust. At one stage the shares reached £17/1s/- each, making them worth more than £6 million. The company also worked a rich gold mine at Matakanui, Central Otago, New Zealand, through its subsidiary the Mount Morgan Sluicing Company.
In 1889, with a substantial fortune, D'Arcy and his family moved to England, where he bought the Stanmore Hall mansion, Bylaugh Park, and a house on Grosvenor Square. His wife, Elena, died in 1897 and, in 1899, he married Nina Boucicault, with whom he lavishly entertained guests. He had acquired a strong interest in horse-racing while in Australia, and maintained a private box at Epsom racecourse. In 1900, he agreed to fund a search for oil and minerals in Persia headed by Wolff, Ketabchee and Cotte. Negotiations with the Mozaffar al-Din Shah Qajar began in 1901, and with the offer of £20,000, for a sixty-year concession to explore for oil— later, the D'Arcy concession —was secured in May, covering, and stipulated that D'Arcy would have the oil rights to the entire country except for five provinces in Northern Iran. In exchange, the Iranian government was given 16% of the oil company's annual profits, an agreement that would haunt the Iranians up until the late 20th century. After the D'Arcy concession, the British became much more concerned with the stability of Iran because of their reliance on the country's vast oil reserves. A drilling team under George B. Reynolds was sent to Persia and began to search, then, in 1903, a company was formed, and D'Arcy had to spend over £500,000 to cover the costs. False hopes were raised in 1904, and D'Arcy was forced to find further financial support, with the Burmah Oil Company Ltd. agreeing to put up to £100,000 into the venture, in return for much of the stock. Drilling in southern Persia at Shardin continued until 1907, when the search was switched to Masjed Soleyman, in a place named Maydon-e-Naftune. Drilling began at one site in January 1908, and at another nearby in March. By April, with no success, the venture close to collapse, and D'Arcy almost bankrupt, he decided, with Burmah, to abandon exploration in Iran. In early May 1908, they sent Reynolds a telegram stating that they had run out of money and ordering him to "cease work, dismiss the staff, dismantle anything worth the cost of transporting to the coast for re-shipment, and come home". Reynolds delayed following these orders and in a stroke of luck, struck oil at shortly after on 26 May 1908. In April 1909, D'Arcy was appointed a director of the newly founded Anglo-Persian Oil Company, which would later become British Petroleum. By 1911, APOC had run a pipeline from the find to a refinery at Abadan. In 1912, the Mount Morgan company was listed in London, and D'Arcy was made chairman of that board. The financial support given by Burmah Oil and the British Admiralty meant that D'Arcy could no longer put his name to the new company despite the best efforts of his wife, and so was a shareholder.