Fuad Masum was born in the city of Koya. He was the son of Sheikh Mohammed Mullah Fuad Masum, a former head of the Association of Muslim Scholars in Kurdistan, who belongs to an established political dynasty with Muslim clerical links. His family descends from the village of Khabanen, which is part of Hawraman. He studied at various religious schools in Iraqi Kurdistan until the age of 18. He studied law and Sharia at Baghdad University. In 1958, Masum traveled to Cairo to complete his higher education at Al-Azhar University. He worked as a professor in Basrah University in 1968. He earned his PhD in Islamic philosophy from Al-Azhar in 1975.
Masum joined the Iraqi Communist Party in 1962, until 1964, where he travelled to Syria to meet the Communist Party secretary there, Khalid Bakdash. After Masum discovered Bakdash's attitudes against the Kurds, he quit the party to join the Kurdistan Democratic Party (PDK).
In 1968, Masum was the PDK representative in Basra. He was also the representative of the Kurdish Revolution in Cairo until 1975.
Masum was one of the founders of the Patriotic Union of Kurdistan (PUK) in 1976. By 1992, he was the first prime minister of Kurdistan. In 2003, following the invasion of Iraq, Masum returned to Baghdad to be a member of the delegation representing Kurdistan, and was a member of the constitution drafting committee. In 2010, Masum became the first Speaker of the Council of Representatives.
In 2014, he was elected by the parliament representatives as the seventh president of Iraq. Masum won 211 votes while his closest competitor, Barham Salih, a former prime minister of Iraqi Kurdistan from October 2009 to April 2012, only received 17. The decision was made during a secret vote of Kurdish MPs, who traditionally have control over the presidency for the sake of political balance. United Nations Secretary-General Ban Ki-moon was present in Iraq when the decision was made, meeting with Prime Minister Nouri al-Maliki about the need for a more inclusive government. Masum accepted the position, noting the "huge security, political and economic tasks" he faces as president.
On 26 August, Masum appointed a new prime minister, Haider al-Abadi.
Masum's appointment of Haider al-Abadi as new prime minister was considered illegal by Nouri al-Maliki and in violation of the constitution. Maliki said that in spite of his erosion of power it was his duty to remain in power because the appointment was a conspiracy rooted from outside of Iraq. Al-Maliki referred the matter to the federal court claiming, "the insistence on this until the end is to protect the state." However, on 14 August 2014, in the face of growing calls from world leaders and members of his own party, the embattled prime minister announced he was stepping down, paving the way for al-Abadi to take over.
Masum is married to Rounak Abdulwahid Mustafa and has five daughters: Shereen (b. 1969), Juwan (b. 1970), Zozan (b. 1977), Shilan (b. 1980) and Veian (b. 1983). He had a son, Showan (1973–1988), who died from a childhood illness.