In the first phase, Sep 10, polls were conducted in seven constituencies, while the rest were held Sep 15.
The elections were necessitated to fill up the seats mostly vacated by sitting legislators to contest the April-May Lok Sabha polls.
The vote is being seen as a mini-referendum for the Nitish Kumar government ahead of state assembly polls slated for next year.
Chief Minister Nitish Kumar, JD-U national president Sharad Yadav, Rashtriya Janata Dal (RJD) chief Lalu Prasad, Lok Janshakti Party chief Ram Vilas Paswan and several central ministers and Congress leaders campaigned for the by-polls.