Zachos was born in Kastoria, Ottoman Empire in 1871 to a family originally from Siatista.
He moved to Germany to study architecture, returning to Greece in 1897 to serve as a volunteer in the Greco-Turkish War.
In 1913, he was involved in drawing up the urban plan of Thessaloniki and from 1915 to 1917 he worked for the Municipality of Athens.
His early works were designed in a conscious "return to our roots" style that included Byzantine Revival buildings such as the cathedral of Agios Nikolaos, the church of Agios Konstantinos, the church of the Transfiguration of the Saviour (all in Volos).
He also blended traditional architecture with contemporary trends in modernism, such as with his Cathedral of the Apostle Paul in Corinth and the Haztimichali House in Plaka.