Mr Rao's successor, Banwarilal Purohit, will be sworn in tomorrow at 9:30 am, the Raj Bhavan said.
At a function held at the airport, Mr Palaniswami and his deputy O Panneerselvam gave a warm send-off to Mr Rao, presenting him with shawls and bouquets.
Mr Rao's year-long tenure was marked by a series of significant developments in Tamil Nadu, including the demise of then chief minister J Jayalalithaa in December 2016 and the subsequent political churn that saw two chief ministers take over within a period of two months.
The Maharastra governor took charge in September 2016 following the retirement of then governor K Rosaiah, days ahead of the hospitalisation of Ms Jayalalithaa in the same month.
His stint saw a split in the ruling AIADMK, following which Mr Palaniswami took over. Later, the rebel faction headed by O Panneerselvam merged with that of Palaniswami. Mr Panneerselvam was since made the deputy chief minister.
Following the August 22 revolt of 19 AIADMK MLAs owing allegiance to sidelined leader TTV Dhinakaran against Mr Palaniswami, the opposition, including DMK, made a beeline to the governor's residence.
They had repeatedly urged Mr Rao to direct a floor test of the Palaniswami government, contending that "it had lost its majority."
Mr Dhinakaran had also called on the governor with a plea to remove Mr Palaniswami as Chief Minister.
Yesterday, Mr Rao had thanked the people of the state for their love, affection and warmth extended to him during his tenure.
He said that in the aftermath of Ms Jayalalithaa's demise, and during the protest for the cause of Jallikattu, "the people of Tamil Nadu had maintained peace and tranquility with great discipline."
Mr Rao left for Hyderabad by a special flight.
Mr Purohit was recently appointed as governor of the state amid calls from various quarters for the presence of a full-time governor.