Earlier this month, Nariman had resigned as solicitor general of India amid speculation that the decision came over his differences with law minister Ashwani Kumar.
Parasaran, a senior advocate of the Supreme Court and son of former attorney general K Parasaran, was appointed as ASG by the first UPA government in July 2004. He continued in office in UPA II.
Last week Parasaran had said that he would be responsive to the "present needs of the society."
He said matters relating to public interest would be his priority.