Born in Chios, he studyied Law at the Athens University and entered the Greek Foreign Ministry after graduation. As a career diplomat, he served in the Permanent Delegation of Greece to the United Nations in New York and NATO in Brussels. He also served in the Greek embassies in Moscow, Pretoria and Ankara.
From 1974 to 1980 Molyviatis was diplomatic advisor and director general of the political cabinet of Prime Minister Constantine Karamanlis.
During the terms of office Constantine Karamanlis as Greek president from 1980 to 1985 and 1990 to 1995, he was secretary general of the Presidential office.
He speaks English and French.
He is chairman of the Konstantinos Karamanlis Foundation.
He is married and has one daughter and one son.