Kiriakos was born in 1811 on the island of Spetses. He was the younger brother of Ioannis Kiriakos, a Vice-Admiral who was killed in the siege of Messolonghi. He studied law at the universities of Pisa and Paris.
In 1835, Kiriakos became public prosecutor of the court of First Instance. In 1843, he helped draft the constitution of Greece. In 1851, he became professor of constitutional law and, in 1862, a member of the committee to draft a new constitution. The following year, Kiriakos became Minister of Religion and Education and, between March and April of that year, Prime Minister of Greece.
Kiriakos authored several books on law and history. He died in Italy in 1869.