Moisiu is the son of the legendary partisan general Spiro Moisiu and embarked on a military career. He attended in the 1950s, a military academy in the Soviet Union and later gained the rank of general. Under the Communist Party leader Enver Hoxha, he was Deputy Secretary of Defense from 1971 and continued in the 1970s, promoted by Hoxha policy of autarky and complete isolation in the military field with order in which the concept of " people's war " dominated. With the formation of 2,000 units distributed in the country in a thickness of 5 to 16 men and an estimated 700,000 bunkers, the country should be protected. Since he is a member of a family that rivaled Hoxha, degraded him this in 1981 for high treason.
After the fall of communism, he became an adviser to the Minister of Defence and Minister of Defense from 1991 to 1992 the transitional government under Vilson Ahmeti. Under the government of Sali Berisha, he was Deputy Secretary of Defense from 1994 to 1997 again. His boss was Safet Zhulali. Then Moisiu led the Atlantic Association, which campaigns for ties to NATO. On 24 June 2002 Moisiu elected by Parliament President of the Republic of Albania. His election was made possible by an agreement concluded with the help of the European Union compromise between the ruling Socialist Party ( SP) of Premier Fatos Nano and the opposition Democratic Party ( PD) of ex- President Sali Berisha.
On 24 July 2002, he succeeds Rexhep Meidani. His tenure ended on 24 July 2007. As the new President, the Vice - Chairman of the Democratic Party, Bamir Topi was elected.
In August 2009, the third volume of Moisius memoirs, in which he devoted his presidency appeared. In his book, he criticized the reigning from 2005 to 2013, Prime Minister Sali Berisha and its predecessor Fatos Nano sharp.
- Midis Nanos dhe Berishës 2002-2007. ( = NE gjurmë të kujtimeve. Vol. 3). Tirana 2009. ISBN 978-99943-1-513-0