Followed by Mr Palaniswami, his cabinet colleagues, including Forest Minister Dindigul Srinivasan, Municipal Administration Minister SP Velumani, Milk and Dairy Development Minister Rajendra Balaji, Speaker P Dhanapal and Leader of Opposition MK Stalin cast their votes.
Of the 234 MLAs in the state, excluding the RK Nagar constituency, which had fallen vacant after the death of former chief minister J Jayalalithaa, all others are eligible to vote.
When asked if DMK chief M Karunanidhi will cast his vote, party's deputy leader in the assembly Mr Duraimurugan told reporters: "Please wait and see till 5 PM."
Mr Karunanidhi is keeping unwell since December last. The voting is taking place in the committee hall at the Assembly Secretariat amid tight security.
Voting began at 10 AM and will continue till 5 PM. Till 11 AM, 120 MLAs had cast their votes, an official said.
Apart from the state MLAs, an MLA from Kerala also voted in Chennai. Union Minister Pon Radhakrishnan, representing Kanyakumari constituency, also voted here.
Besides, rebel AIADMK leader and former Tamil Nadu chief minister O Panneerselvam, former school education minister, Pandiarajan and Semmalai, Congress legislature party leader KR Ramasamy were among those who cast their vote.
Later MLA Ramasamy told mediapersons, "The opposition presidential nominee Meira Kumar has bright chances of winning the poll." Deputy Speaker of the Assembly V Jayaraman said, "Ram Nath Kovind has good chance of winning the poll."
Meanwhile, polling was underway at the territorial assembly in Puducherry, with speaker V Vaithilingam and Chief Minister V Narayanasamy casting their votes.
The NDA has fielded former Bihar Governor Ram Nath Kovind for the top constitutional post, while former Lok Sabha Speaker Meira Kumar is the joint opposition candidate. The tenure of incumbent Pranab Mukherjee comes to an end on July 24.