Irineos was dismissed in May over an alleged multimillion-dollar sale of church land in a mainly Palestinian area of Israeli-occupied east Jerusalem to Jewish investors.
Under church law, Theophilos's 22 August election must be approved by Israel, Jordan and the Palestinian Authority.
Like the Palestinians, Jordan approved Irineos's dismissal, but Israel has steadfastly refused to recognise the move.
The Israeli government had refused to recognise the August 2001 election of Irineos until January 2004.
Theophilos has been archbishop of Tabor since February, after serving as the Church's top clergyman at the Church of the Holy Sepulchre in Jerusalem.
Born in southern Greece in 1952, he arrived in the Holy Land in 1964 to study theology and was ordained a priest in 1970.