Neocleous graduated from National and Kapodistrian University of Athens Law School in 1964. He began practicing law in 1965 and has specialized in the fields of international investment and international corporate tax law. He was the founder and managing partner of Andreas Neocleous & Co LLC.
In 1970, he was elected as a member of the Parliament of the United Party (Eniaion Party) in Cyprus and served till 1976.
In 2017, Neocleous's law firm Andreas Neocleous & Co, among others, was found guilty of bribing a deputy attorney general of Cyprus. Shortly thereafter, the law firm changed its name to Elias Neocleous & Co LLC.
In 2019, Neocleous bought the Cyprus Mail. Criticism came when articles referring to his former law firm's conviction were removed from the website of the newspaper the day after ownership of the newspaper changed.
Neocleous was married to Lia, and they had two children, Elias and Panayiotis, both lawyers.
He was an honorary fellow of the Center for International Legal Studies. He was the Honorary Consul of Japan in Cyprus and the honorary legal adviser of the British High Commissioner in Cyprus.
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