They are among the six candidates in the fray for as many vacancies in the Upper House from the state.
Former Union minister Praful Patel (NCP), BJP's Vinay Sahasrabuddhe and Vikas Mahatme and Shiv Sena's Sanjay Raut have also filed their papers since the process for the biennial elections got underway.
The scrutiny of papers will be held tomorrow.
Formal announcement on their election will be made on June 3, the last date of withdrawal of nominations, a senior Vidhan Bhawan official told PTI.
His son Karti Chidambaram was also present.
Chidambaram did not contest the 2014 Lok Sabha polls while his son Karti had unsuccessfully fought from his native Sivaganga constituency in Tamil Nadu.
Meanwhile, former Maharashtra Chief Minister Narayan Rane filed his nomination papers here for a Rajya Sabha seat.
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