"RJD will support the JD-U government led by ... Manjhi," Siddiqui, the RJD legislature party leader in the assembly, told IANS.
Siddiqui said a formal announcement would be made at a meeting of RJD legislators Thursday evening.
The RJD has 21 members in the 243-member state assembly.
The new chief minister, who succeeded Nitish Kumar, said he was happy to get the Rashtriya Janata Dal's legislative backing.
"It is nice to hear that the RJD will support my government," he said.
Two days ago the Congress extended support to the JD-U government. The Congress has four legislators.
Nitish Kumar resigned Saturday following his party's debacle in the Lok Sabha polls.
The JD-U has 117 legislators and also enjoys the support of one CPI member and two independent legislators.