The tenure of Rosaiah ended on August 31.
Maharashtra Governor C Vidyasagar Rao was given additional charge of Tamil Nadu.
Rosaiah replaced Surjit Singh Barnala in 2011 by then Congress-led government at Centre.
Rosaiah, a former Andhra Pradesh Chief Minister, was given a farewell by State government officials led by Finance Minister O Panneerselvam ahead of his departure, official sources said.