The 32-year-old batsman has not featured in a Test for his country since suffering a home series defeat to England in late 2012.
Gambhir is part of an 18-man squad that also includes inexperienced duo Pankaj Singh and Stuart Binny, while there is no place for left-arm seamer Zaheer Khan or batsman Robin Uthappa.
Ishant Sharma keeps his place, and Varun Aaron returns to the fold.
Suresh Raina will captain the one-day side on their tour of Bangladesh, having been recalled after missing out on the Asia Cup.
The Chennai Super Kings man has not played a one-day international since India’s 4-1 series demolition at the hands of New Zealand in January.
The opening ODI against Bangladesh takes place on June 15, before the Test series in England gets under way on July 9.
India squad for ODI series in Bangladesh:
Suresh Raina (Captain), Robin Uthappa, Ajinkya Rahane, Cheteshwar Pujara, Ambati Rayudu, Manoj Tiwary, Kedar Jadhav, Wriddhiman Saha, Parvez Rasool, Akshar Patel, Vinay Kumar, Umesh Yadav, Stuart Binny, Mohit Sharma, Amit Mishra.
India squad for Test series in England:
MS Dhoni Captain, Murali Vijay, Shikhar Dhawan, Gautam Gambhir, Cheteshwar Pujara, Virat Kohli, Ajinkya Rahane, Rohit Sharma, Ravindra Jadeja, R Ashwin, Bhuvneshwar Kumar, Mohammed Shami, Ishwar Pandey, Ishant Sharma, Stuart Binny, Varun Aaron, Wriddhiman Saha, Pankaj Singh.
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