Nadda was born on 2 December 1960 in Patna, Bihar in the family of Narain Lall Nadda and Krishna Nadda, with roots in Himachal Pradesh. He belongs to Brahmin community. He has a brother named Jagat Bhushan Nadda.
Nadda was educated at St. Xavier's School, Patna. Thereafter he did his B.A. from Patna College, Patna University and LL.B. from Faculty of Law, Himachal Pradesh University, Shimla. As a child, he represented Bihar in the All India Junior Swimming Championship held at Delhi.
Nadda married Mallika Nadda (née Banerjee) on 11 December 1991, with whom he has two sons. His mother-in-law Jayashree Banerjee was elected to Lok Sabha in 1999.