Nitish Kumar was on Sunday chosen as the leader of the National Democratic Alliance, which has won 125 seats in the 243-member Bihar Assembly.
Nitish Kumar later went to the Governor's House in Patna to present a list of 125 newly elected MLAs to Governor Phagu Chauhan to lay his claim for the formation of the new government.
Nitish Kumar and his Ministers in the new Cabinet were expected to take oath on Monday.
In a related development, Sushil Kumar Modi was elected as leader of BJP Vidhan Mandal (legislature) in Bihar. However, the decision on the Deputy CM is not yet clear.
A decision on Nitish's name was taken at a meeting of newly elected MLAs of the National Democratic Alliance partners BJP, JD-U, Hindustani Awam Morcha and Vikassheel Insaan Party at the official residence of Nitish Kumar, who is set to return as the Chief Minister for the fourth consecutive term.
Senior BJP leader Rajnath Singh made the announcement on Nitish's election.
Earlier, Nitish was elected as the Janata Dal-United Legislature Party leader in the new Bihar Assembly. He was re-elected to the post at a meeting of the newly elected MLAs of the JD-U and the MLCs at the CM residence here.