Tsege was born in Addis Ababa, Ethiopia on 9 February 1955. He is one of nine children and grew up in a household that was a sanctuary to the disadvantaged. His mother, a teacher by profession, had great empathy for people in need and was always helping. She was Andargachew's inspiration for his lifelong commitment to fight for social justice. During his high school years in Teferi Mekonnen School and later as an Electrical Engineering student at Addis Ababa University, he became very active in the student movement.
Following the Ethiopian revolution of 1974 when a military dictatorship, Derg, seized power he joined the Ethiopian People's Revolutionary Party (EPRP) and went underground, like most of the Ethiopian youth, in their struggle against the Marxist regime. During the Derg’s Red Terror campaign of 1974, his younger brother Amha Tsege was murdered by the security forces and Andargachew fled Ethiopia. Later, due to an ideological difference in the EPRP party, Tsege crossed into Sudan. In 1979 he was granted asylum in the United Kingdom (UK), where he later gained citizenship.
In the UK he studied philosophy at University of Greenwich in the early 1980s and wrote his dissertation on the German philosopher Immanuel Kant.
When Derg was overthrown in 1991, Tsege went back to Ethiopia to help the newly formed Ethiopian People's Revolutionary Democratic Front (EPRDF) government led by his former university friend Meles Zenawi. Within two years, he was disillusioned with the ethnicity-oriented politics advocated by EPRDF and left the government. He moved back to London and started writing articles that were critical of the regime and its divisive politics.
In 2005, Tsige returned to Ethiopia and published a book in Amharic which loosely translates to "Freedom fighter who does not know freedom", an analysis of the state of Ethiopian politics at the time. Soon, with an invitation from then deputy leader of Coalition for Unity and Democracy (CUD) party Berhanu Nega, he joined the party and helped the party in the ill-fated election of May 2005.
In June 2005, Tsige was imprisoned during the crackdown by the Ethiopian government after the election.
After his release, he returned to London, where he was able to campaign against the regime by testifying at different government or international organisations including the US congress and European Union Human Rights committee as well as think tanks such as Chatham House. He became the principal spokesperson for the CUD party in exile and was instrumental in mobilizing the global Ethiopian diaspora for a worldwide campaign to secure the release of the CUD leaders and all prisoners of conscience.
In May 2008, he founded Ginbot 7 Movement for Justice, Freedom and Democracy with Berhanu Nega, one of the exiled leaders of CUD. He was elected as Secretary General of Ginbot 7.
On 22 December 2009, an Ethiopian court sentenced Tsige to death, in absentia, while 33 others were sentenced to life in prison along with four others who were also sentenced in absentia.
On 7 November 2013, Ginbot 7 claimed it foiled an assassination plot that targeted Tsige, secretary of Ginbot 7, as well as commanders and high-ranking officers of Ginbot 7 Popular Force.
On 23 June 2014, he was once again imprisoned by the Ethiopian regime. He was arrested by Yemeni security forces, in collaboration with Ethiopian intelligence service members, at Yemen's Sana'a International Airport while in transit from the United Arab Emirates to Eritrea. He was detained in an unknown location and no official statement was forthcoming from either the Yemeni or Ethiopian governments.
In February 2015, an early day motion was tabled within the UK parliament, recognising Tsige's 60th birthday, and calling for pressure to be applied to the Ethiopian government, in order to secure his release. In October 2016 Tsige's family wrote to ex British Prime Minister Tony Blair to use his "advisory role with the Ethiopian government" to call for Tsige's release. Blair's Tony Blair Africa Governance Initiative has an embedded team of advisors in Ethiopia.
Andargachew is married to British citizen Yemserach Hailemariam (Yemi). They have three children together (Hilawit, Menabe and Yilak). His family continue to live in London. In 2015 Hilawit awarded the Christine Jackson Young Person Award by the charity Liberty in recognition of her ongoing battle for the release of her father. Andargachew is a fan of Arsenal FC.