Horta e Costa studied at the Escola do Exército and started his military career as an Alferes of engineers on 10 January 1883. He belonged to the general staff of his military branch and was promoted through lieutenant, captain, major, and lieutenant colonel, finally reaching the post of colonel of engineers. At the University of Coimbra he took a bachelor's degree in mathematics. A lieutenant already in 1886, the Minister of the Navy, Manuel Pinheiro Chagas, appointed him director of public works of Macau. Here he distinguished himself, and in 1888 he was elected deputy to the Cortes Gerais for the legislature of 1887-1889 in a supplementary election, taking his seat in 1889 already with the post of captain, in which seat he had interventions on 23 and 30 January, 10 and 21 April, 3 May, 6, 14 and 26 June 1889. He had a seat at the Chamber in diverse legislatures, more specifically in the ones of 1890-1892 and 1893, in which he was part of commissions twice in 1892, thrice in 1893 and thrice in 1894 and had interventions on 7 June, 11, 15 and 21 July and 21 August 1890, 22 June 1891, 3 February and 19 March 1892, 10 January, 22, 23 and 27 May, 20, 22 and 23 June and 1, 5, 6 and 12 July 1893, always representing the circle of Macau, where he returned in 1893 as 69th governor, taking office on 24 March 1894. He resigned on 12 March/May 1897 after a ministerial change and was granted a Letter of Counsel, becoming a Member of His Most Faithful Majesty's Counsel. He was also an and a minister plenipotentiary in China, Japan, and Siam, where he met the Empress Dowager Cixi and Guangxu Emperor at the Forbidden City in Beijing; Emperor Meiji in Tokyo; and Chulalongkorn in Bangkok, who decorated him. In 1900 the Regenerator Party returned to power and the Counsilor Horta e Costa was again appointed on 12 August as the 71st Governor of Macau, where he conducted a military expedition. The mission was difficult and risky, and he received a Portary of Commendation. He then founded the Lyceum and made various improvements. He left office on 17 December 1902. On 14 February 1907, as Chief of Cabinet of the President of the Ministry of João Franco, he was appointed 113th Governor-General of India, an office he bore until the proclamation of the Portuguese Republic in 1910. In the year he took office he instaured an enquiry. His government was marked by the promulgation of various measures towards developing commerce in the province. One of the most important improvements achieved in his tenure was the building of metal bridges to improve the communication between cities in the province. Among other achievements, he regularised the water supply in Panaji city by building a special reservoir at Bainguinim with special imported materials from France. He also increased the capacity of the port at Mormugão and he was responsible for Campal Avenue, where he constructed roads with footpaths and planted trees. According to GoanhistorianPercival Noronha, the fact that he was an engineer by profession made a difference, and the amount of development work carried out by him in the four years of his rule was something "never done in hundreds of years". He also had other plans which were not fulfilled during his regime. His government was marked by the Revolt of the Ranes, to which the simple arrival of a company of Landins was enough to overcome. With the Proclamation of the Portuguese Republic he ended his term. A public political rally elected Dr. Francisco Manuel Couceiro da Costa as the new governor, as required by the provisional government. Horta e Costa embarked for his homeland without being molested and with the respect of all the population of India. Avenida Horta e Costa, in Macau, is named after him.
He married Carolina Adelaide Pinheiro de Vasconcelos Silvano on 12 April 1886, shortly before embarking to Macau, daughter of António Maria Silvano, then a Lieutenant Colonel of the Infantry Regiment of the Overseas, later Brigadier General and General of the Arm of Infantry, Knight and Officer of the Order of Aviz, Commander of the Order of Isabella the Catholic, etc., and his wife Carolina Xavier Pinheiro. They had three children:
