She resigned after the Supreme Court Collegium declined to reconsider its decision to transfer her to the Meghalaya High Court two days ago.
The collegium, headed by Chief Justice of India Ranjan Gogoi, recommended transfer of Justice Tahilramani to the Meghalaya High Court.
She was elevated as the Chief Justice of Madras High Court in August last year.
She was to retire on October 2, 2020.
Justices Tahilramani and Gita Mittal were the only women chief justices in the male-dominated 25 HCs.
Justice Tahilramani, in her one-paragraph resignation letter, requested President Kovind to relieve her immediately.
President Kovind has forwarded the letter to the government for further action.