The 68-year-old Manjhi, a dalit leader, was SC & ST minister in the Nitish Kumar government.
The JD(U) has staked claim to form the government in the state under Manjhi, Kumar said.
Manjhi's name, he said, has the approval of JD(U) President Sharad Yadav as well state party chief Basistha Narayan Singh.
"We have staked claim before Governor D Y Patil to form the government under leadership of Jitan Ram Manjhi," outgoing Chief Minister Nitish Kumar told reporters outside Raj Bhawan.
He said "We have handed over a list of support of 117 JD(U) MLAs, 2 Independents and 1 CPI member totalling 120 to the Governor for formation of the new government." Asked for the reason for choosing Manjhi as his successor, Kumar said "he is experienced and his contribution to the party is immense."
The effective strength of the House at present is 239.
JD(U) has 117 members, BJP 90, RJD 21, Congress 4 and others including Independents 1 CPI member 7.
The four-member Congress, which voted for the Nitish Kumar government in the trust motion in June last year has authorised party High Command to decide on the future course of action.