Mr Naidu was the first to cast his vote followed by Mr Kodela at the polling booth in the state Assembly's committee hall.
The ruling Telugu Desam Party MLAs then cast their votes.
The four BJP MLAs also cast their votes along with their ally.
Leader of Opposition and YSR Congress president YS Jaganmohan Reddy led his party MLAs in the polling process.
All the 175 MLAs in the AP Assembly, including those of the lone opposition YSRC, had earlier pledged their support to NDA's presidential candidate Ram Nath Kovind.
From Andhra Pradesh, the Congress has only four members in the Rajya Sabha and none in the Lok Sabha and the state Assembly.