Damodaran, 77, died at a private hospital where he was undergoing treatment for nearly a month for respiratory ailment, they said.
He leaves behind wife and a daughter.
A senior advocate of the state high court, Damodaran had functioned as Advocate General during the LDF regime headed by E K Nayanar from 1996-2001.
Condoling his death, Chief Minister, Pinarayi Vijayan, said Damodaran had always stood for the people's cause.
Recalling his stint as A-G, Vijayan said Damodaran's services would always be remembered.
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The present LDF government had last year initiated steps to appoint Damodaran as the legal advisor to the Chief Minister.
However, the move was given up following protest by opposition Congress-led UDF which had referred to Damodaran's appearance for controversial lottery baron Santiago Martin and some quarry owners in different cases in the high court.
Damodaran was imprisoned during the Emergency in 1975-77.