Harbhajan, 34, whose 413 wickets in 101 internationals make him the most successful current spinner in the game, last played for his country in the Hyderabad Test against Australia in March 2013.
“With several left-handers in the Bangladesh team, we decided to go in with two off-spinners in Harbhajan and Ravichandran Ashwin in the Test squad,” said chairman of selectors Sandeep Patil.
India named full-strength Test and one-day international squads for the short tour, despite media speculation that senior players may be rested after being on the go since October.
Injured seamer Mohammed Shami was the lone omission as the selectors picked the same ODI squad which reached the World Cup semi-finals under Mahendra Singh Dhoni’s captaincy earlier this year.
Virat Kohli, who took over the Test captaincy after Dhoni retired from the longer format during the tour of Australia, was reappointed captain for the lone Test match in Fatullah from June 10.
The Test will be followed by three ODIs in Dhaka on June 18, 21 and 24.
India Test squad: V Kohli (capt), M Vijay, S Dhawan, L Rahul, C Pujara, A Rahane, R Sharma, W Saha, R Ashwin, H Singh, K Sharma, B Kumar, U Yadav, V Aaron, I Sharma.
India ODI squad: MS Dhoni (capt), R Sharma, A Rahane, S Dhawan, V Kohli, S Raina, A Rayudu, R Ashwin, R Jadeja, A Patel, B Kumar, U Yadav, M Sharma, S Binny, D Kulkarni.