Chief Minister and BJD President Naveen Patnaik announced Singhdeo and Singh's names for the by-poll which is slated to be held on July 3.
The by-elections were necessitated following the election of party leaders Sashi Bhushan Behera and Rabinarayan Mohapatra to the state Assembly in the recently-held polls.
While Behera was elected from the Jaydev Assembly segment, Mohapatra won the Ranapur seat.
Singhdeo, who is considered to be close to Patnaik, contested the Assembly polls from Bolangir but was defeated by Congress stalwart Narasingh Mishra.
BJD, which has 117 legislators in the 147-member Assembly, is in a strong position for the by-polls, to the Upper House of Parliament.
On June 12, BJD candidate and Odia film actor Anubhab Mohanty was elected unopposed to Rajya Sabha after the nomination papers of the other two candidates were rejected.
Their papers were rejected during scrutiny on June 10 since they did not have the requisite number of proposers, sources said.
