EC Secretary Md Alamgir made the announcement after a meeting of the commission.
There is no need for submitting nomination papers newly, he said, adding that activities will resume from where the election was suspended.
Earlier, EC had postponed by-polls in the two constituencies slated for March 29 due to coronavirus.
Constitutionally the Election Commission is bound to hold an election by 180 days after postponement.
Accordingly, the time limit for holding voting in Bogura-1 ends on July 15 while Jashore-6 on July 18.