He was born in a small village called Garissa in the Lughaya district of northern Somalia. He was into the politically powerful Mamassan subclan of the Issa clan.He played an important role in Djibouti's struggle for independence from France. According to I.M. Lewis, "with the powerful support of the French electorate" Hassan Gouled campaigned against Mahamoud Harbi Farah of the Union Republicaine party, who sought to join the territory with neighboring Somalia. By the time of the 23 November 1958 elections, Mahamud Harbi's party had disintegrated and with the majority of the Afar vote, his faction won election. Mahamud Harbi subsequently fled Djibouti, and later died in a plane crash.[
Hassan Gouled served as Vice-President of the Government Council from 1958 to April 1959. Hassan Gouled also served in the French National Assembly 1959-1962 and the French Senate 1952-1958. He was Minister of Education in Ali Aref Bourhan's government from 1963 to 1967. Later he served as Prime Minister between May 1977 and July 1977.

In the 1990s, the Djibouti economy deteriorated dramatically, with net external assets falling by 40 per cent. The World Bank issued "a correspondingly gloomy and highly critical" assessment, mentioning such social problems as the excessive consumption of the addictive and debilitating drug qat by Djibouti's citizens. During this period, Hassan Gouled's nephew Ismaïl Omar Guelleh not only maneuvered to be his successor, but increasingly came to handle affairs for the elderly Hassan Gouled.
On 4 February 1999, Gouled Aptidon announced that he would retire at the time of the next election, and an extraordinary congress of the RPP chose Guelleh as its presidential candidate. Guelleh won the presidential election held in April 1999 and succeeded his uncle on 8 May 1999. Gouled Aptidon died at his home on 21 November 2006, aged 90.
Gouled's first wife, former First Lady Aicha Bogoreh, a proponent of women's rights and various charities, died in 2001.He married his second wife after Bogoreh's death.