Tejaswi Yadav, a former cricketer, is the younger son of Rashtriya Janata Dal chief Lalu Prasad.
Earlier, the RJD's 80 legislators authorised Lalu Prasad to choose the leader in the house.
The RJD is the biggest party in the tri-party Grand Alliance, which also includes Chief Minister Nitish Kumar's Janata Dal-United (JD-U) and the Congress.
Lalu Prasad earlier said that Tejaswi Yadav will play an important role in the new Bihar government.
The RJD won 80 assembly seats followed by the JD-U with 71 and the Congress with 27 seats. The BJP bagged 53 seats and its three allies five seats.