The two leaders also recalled the contribution of the leader in the political domain, both as Chief Minister of Maharashtra and later as a member of the Union cabinet.
"I am deeply shocked and grieved to hear about the demise of your beloved husband. He was an able administrator who was known for his simplicity and dedicated his life for uplift of the poor and downtrodden in villages," Rosaiah said in his condolence message sent to Vaishali Deshmukh, wife of the deceased.
The governor recalled the political career of the late Deshmukh and his rise from being a Zilla Panchayat member to becoming the Chief Minister.
"His death is an irreparable loss to the nation and to the people of Maharahstra in particular," he said.
Jayalalithaa also expressed grief and shock over the leader's demise at a city hospital.
"In his life time he played a crucial role in the Indian National Congress. As a member of the Rajya Sabha, representing Maharashtra, he brought a quiet dignity to his role in the Upper House. As a Chief Minister, he steered his state with sagacity and a maturity which was appreciable," she said in a statement.
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"I offer my sincere and heartfelt condolences to his family and pray that the Almighty may give them the strength to cope with this irreparable loss," she added.
Meanwhile, describing Deshmukh as a tall leader of Maharashtra and an important personality, senior Congress leader and Union Minister of State in PMO V Narayanasamy said that his death "is a great loss to the party and the government."
Condoling his death, he said that Deshmukh had held several important positions and proved his capability.