India had suspended the flights nearly eight months ago when the virus outbreak began to spread.
The flights will connect five Indian cities with Dhaka, the Indian High Commission in Dhaka tweeted on Saturday.
Initially, around 5,000 passengers from both the countries would be able to fly each week, the report quoted Civil Aviation Authority of Bangladesh (CAAB) Chairman Air Vice Marshal M. Mafidur Rahman said on Sunday.
There is no transit facility for the passengers to fly to a third country, he said, adding that the passengers would have to undergo Covid-19 testing before flying.
On October 9, the Indian High Commission in Bangladesh announced resumption of online visa application services for Bangladeshi citizens.
For now, visas will be provided in nine categories, including medical, business, employment, journalists and diplomats.
Three airlines from Bangladesh will operate 28 flights a week initially, while five Indian airlines will operate the same number of flights, the Bangladesh foreign ministry said on Facebook.
The Bangladeshi airlines are Biman Bangladesh Airlines, US-Bangla Airlines, and NOVOAIR, while the Indian airlines are Air India, Vistara, IndiGo, SpiceJet, and GoAir.
Biman is scheduled to operate flights on Dhaka-Delhi-Dhaka and Dhaka-Kolkata-Dhaka routes, US-Bangla Airlines on Dhaka-Chennai and NOVOAIR on the Dhaka-Kolkata-Dhaka route.
The Indian airlines will operate flights on Dhaka-Delhi-Dhaka, Dhaka-Kolkata-Dhaka, Dhaka-Chennai-Dhaka, and Dhaka-Mumbai-Dhaka routes.
It had also suspended visas in March and resumed the online application services for Bangladeshis last week.
The suspensions spelt trouble for many Bangladeshis who needed to travel to India, especially to get medical attention.
In normal days, more than 3,500 Bangladeshis travel to India daily on an average. Over 10 per cent of them travel on medical purposes.
Of the foreigners who visit India for medical purposes, 45 per cent are from Bangladesh, according to the India-Bangladesh Chamber of Commerce and Industry.
More than 13.7 million foreigners took treatment in India between January 2018 and March 2019. They include 2.8 million Bangladeshis.
After arriving in Dhaka earlier in October, Indian High Commissioner Vikram Kumar Doraiswami said India was committed to deliver on a special "air bubble" arrangement to resume aviation "very soon" as promised by Indian Foreign Secretary Harsh Vardhan Shringla during his Dhaka visit in August.