Tamil Nadu Governor Ch Vidyasagar Rao administered the oath of office to Justice Banerjee at a ceremony held at Raj Bhavan.
Chief Minister K Palaniswami was also present during the swearing-in ceremony.
Earlier, Banerjee (59) served as a judge in the Delhi High Court and her appointment came following the elevation of former Chief Justice of Madras High Court, Sanjay Kishan Kaul, to the Supreme Court in February.
Justice Banerjee enrolled as an advocate in 1985 and practiced both in the original and appellate sides of Calcutta High Court in all branches of law except criminal.
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Later, the Chief Justice, who was given a warm welcome by the Advocate General and presidents of various advocates associations, said she hoped live up to the expectations of the legal fraternity.
"I do not have enough words to express my gratitude. I thank you for the warm welcome. I assure you that I will try my best to live up to your expectations," she said.
Banerjee further said she was really glad that she had the opportunity to learn Tamil and read some (Tamil) literature.