The Siwan Local Authority Constituency seat fell vacant following resignation of Manoj Kumar Singh, while a general seat fell vacant after sitting MLC Gulam Gaus quit. Both of them resigned in April.
The term of the Siwan MLC was to have expired in July, 2015, and that of the other legislator in July, 2016.
The notification will be issued on August 25, while September one will be the last date of filing nominations.
Counting of votes will be held soon after polling on September 11, EC said in a statement.