The election for the seats is scheduled for later this month.
Bihar JD-U president Vashisht Narain Singh told reporters here: "The party has nominated Yadav, Baliyavi and Verma for by-election and will file their nomination papers Monday."
Sharad Yadav lost the Lok Sabha election from Madhepura constituency last month.
To ensure his presence in parliament and active role in the national politics, the JD-U has decided to send him to the Rajya Sabha, a senior party leader said.
Baliyavi is a Muslim face of the JD-U while writer-author and former diplomat Pawan Verma is a sophisticated face of the party in Delhi.