Mr Madhusudanan, an MGR loyalist, was the Textiles Minister during Ms Jayalalithaa's first term between 1991 and 1996. He had then won from the same R K Nagar constituency.
The announcement comes a day after the ruling AIADMK announced VK Sasikala's nephew and party's number two, TTV Dinakaran as their candidate.
Mr Madhusudanan told NDTV, "I am a local person here. I have been residing here for the past 56 years. I have also contested in RK Nagar. I have done many more things for the constituency."
As things stand now, RK Nagar would see a four-cornered contest. The DMK has announced Marudhu Ganesh as its candidate. Jayalalithaa's niece Deepa Jayakumar too has thrown her hat for Ms Jayalalithaa's legacy. The BJP is likely to contest as well.
The stakes are high as the by-poll could establish who would inherit Jayalalithaa's political legacy among her jailed aide VK Sasikala, O Panneerselvam and Deepa Jayakumar. The DMK which lost the seat last time is hopeful too, banking on the likely fragmentation of AIADMK votes. The results would also set the trend for the upcoming local body polls.
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.