The 34-year-old Harbhajan, who last played in a home test series against Australia in March 2013, was picked on Wednesday in the Virat Kohli-led side despite limited success in first-class cricket this past season.
Harbhajan, who has 413 wickets from 101 tests, finds himself in the team along with regular test offspinner Ravichandran Ashwin.
Mahendra Singh Dhoni, who has retired from test cricket, will lead the ODI squad.
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The selectors have announced full-strength sides for the test and ODIs.
The test will be at Fatullah from June 10-14, with the ODIs scheduled at Mirpur on June 18, 21 and 24.
