Zimbabwe will play all the four ODIs at the Harare Sports Club.
Meanwhile, Brendan Taylor scores twin tons but goes vain as Mehidy Hasan levels series.
Mahmudullah scored his first Test century in more than eight years as Bangladesh set Zimbabwe a towering 443-run target.
Zimbabwe were bowled out for 304 runs in the first innings of the second Test against Bangladesh on the third day in Dhaka on Tuesday.
Zimbabwe reached 25-1 at stumps after Bangladesh declared their first innings of the second Test at 522-7 on day two in Dhaka on Monday.
Mominul Haque, Mushfiqur Rahim score tons to give Bangladesh first-day honours.