Koutsogiorgas was born in May 1922 in the village of Rodini in Achaea. During the Axis Occupation of Greece in the Second World War, Koutsogiorgas was active in the Omiros resistance group, and was arrested and imprisoned by the Italian occupation authorities. He studied at the Law School of the University of Athens, and received his law degree in 1945. That same year, he became a police officer in the Athens branch of the City Police. He served as a police officer for seven years, until he resigned in 1952, in order to become a lawyer and open his own law firm. In 1958 he obtained a postgraduate degree in Public Law from the Law Faculty of the University of Paris.
In the post-war era, he became a prominent Athens lawyer, and was closely associated with Georgios Papandreou, the leader of the Liberal Party and later of the Centre Union. During the ASPIDA scandal of 1965, he was defence attorney to the Georgios Papandreou's son, Andreas Papandreou.
During the Greek military junta of 1967–1974, Koutsogiorgas participated in attempts to organize armed resistance against the regime as early as 1967, and was arrested and imprisoned after arms and radio transmitters were discovered at his home. He was later released, but re-arrested in 1970 and held for a while, undergoing interrogation by the infamous EAT-ESA.
He was elected Member of Parliament in the first national election that took place in November 1974 after the fall of the military government. He held a parliament seat for the prefecture of Achaea in all successive national elections until 1989. In the first PASOK cabinet, Koutsogiorgas was appointed Minister to the Presidency of the Government on 21 October 1981, a post he held until 17 January 1984, when he was named Minister for the Interior. He held the post until resigning on 9 May 1985 before the parliamentary elections, with the exception of the period 22 May – 21 June 1984, when he was replaced by an acting minister for the European Parliament election. During this time he played a major role in the March 1985 political crisis over the issue of the re-nomination of then-President of Greece Constantine Karamanlis for a second term. Papandreou had promised it several times, but the PASOK party base and Koutsogiorgas himself fiercely opposed it. Eventually, largely through Koutsogiorgas insistence PASOK proposed the judge Christos Sartzetakis for the post.