India have not hosted Bangladesh for a Test match since the Tigers gained full status in 2000. Bangladesh's only visits to India have been for one-day internationals.
India have played seven Tests in Bangladesh, including the inaugural match in Dhaka in November 2000, but remain the only Test-playing nation yet to welcome the Bangladeshis at home.
Bangladesh cricket chief Mustafa Kamal informed his colleagues in the BCB that he had been assured by his Indian counterpart Narayanaswamy Srinivasan that India will host Bangladesh this year.
Kamal met Srinivasan on the sidelines of the Indian Premier League tournament and he had "received assurance that India will host Bangladesh for a full tour later this year", a BCB statement said.
There was no immediate comment from the Board Of Control For Cricket In India, and it remained unclear how India will accommodate Bangladesh in their crowded schedule.
India are due to host New Zealand in August-September for three Tests, take part in the World Twenty20 in Sri Lanka in September-October, and then host England for four Tests in November-December.
Bangladesh have lost 63 of their 73 Tests so far, winning only three, but opener Tamim Iqbal hopes his country will get to play five-day matches on a regular basis.
"If we want to really improve in Test match cricket, we need to play the format a lot more," Tamim, who is in India for the IPL, was quoted as saying by the Cricinfo website.