Queirós was born in Évora, Portugal in 1565. As a young man he entered Spanish service and became an experienced seaman and navigator. In April 1595 he joined Álvaro de Mendaña de Neira on his voyage to colonise the Solomon Islands, serving as pilot. After Mendaña’s death in October 1595 he is credited with taking command and saving the only remaining ship of the expedition, arriving in the Philippines in February 1596.
In 1598 Queirós returned to Spain and petitioned King Philip III to support another voyage into the Pacific. A devout Catholic, Queirós also visited Rome in 1600, where he obtained the support of the Pope, Clement VIII, for further explorations. He greatly impressed the Spanish Ambassador in Rome, the Duke of Sesa, who described him as a “man of good judgement, experienced in his profession, hard working, quiet and disinterested.”  While in Rome Queirós also first wrote his Treatise on Navigation as a letter to the king, further reinforcing his reputation as a navigator. In March 1603 Queirós was finally authorized to return to Peru to establish another expedition, with the intention of finding Terra Australis, the mythical "great south land," and claiming it for Spain and the Church. Queirós's party of 160 men on three ships, San Pedro y San Pablo (150 tons), San Pedro (120 tons) and the tender (or launch) Los Tres Reyes left Callao on 21 December 1605.
In January 1606 the expedition discovered Henderson Island and Ducie Island. It discovered the Buen Viaje Islands (Butaritari and Makin).
In May 1606 the expedition reached the islands later called the New Hebrides and now the independent nation of Vanuatu. Queirós landed on a large island which he took to be part of the southern continent, and named it Australia del Espiritu Santo. In his printed memorials, notably the Eighth (which was published in Italy, Holland, France, Germany and England), this was altered to Austrialia del Espiritu Santo (The Australian Land of the Holy Spirit), a pun on "Austria", to flatter King Philip III, who was of the House of Austria. The island is still called Espiritu Santo. Here he stated his intention to establish a colony, to be called Nova Jerusalem. He seems to have identified Australia/Austrialia del Espiritu Santo with the huge northward extension of the Austral continent joining it to New Guinea, as depicted in maps like those of Gerard de Jode and Petrus Plancius. For, as he said in his Tenth Memorial (page 5): “It should be noted that New Guinea is the top end of the Austral Land of which I treat".
Queirós's religious fervour found expression with the founding of a new Order of Chivalry, the Knights of the Holy Ghost. The Order’s purpose was to protect the new colony. However, within weeks the idea of a colony was abandoned due to the hostility of the Ni-Vanuatu and to disagreements among the crew.
After six weeks Queirós's ships put to sea to explore the coastline. On the night of June 11, 1606 Queirós in the San Pedro y San Pablo became separated from the other ships in bad weather and was unable (or so he later said) to return to safe anchorage at Espiritu Santo. He then sailed to Acapulco in Mexico, where he arrived in November 1606. In the account of Diego de Prado y Tovar, which is highly critical of Queirós, mutiny and poor leadership is given as the reason for Queirós's disappearance.
Two weeks later, his second-in-command, Luis Váez de Torres, after searching in vain for Queirós and assuming his ship was wrecked, left Espiritu Santo. Torres successfully reached Manila, the center of the Spanish East Indies in May 1607, charting the southern coastline of New Guinea on the way and in doing so sailing through the strait that now bears his name. Full story