India were 2-1 ahead when the final Test at Old Trafford in September was cancelled following COVID-19 cases in their camp. Edgbaston will host the match from July 1.
Pujara, dropped after India's tour of South Africa this year, was picked in the 17-member squad after his four 100-plus scores, including two double hundreds, in five county championship division two matches.
All-rounder Ravindra Jadeja, who missed the final Indian Premier League matches with a rib injury, was also picked alongside fellow spinner Ravichandran Ashwin.
India rested several frontline players, including captain Rohit Sharma and batsman Virat Kohli, and put KL Rahul in charge of an 18-member squad for next month's home T20 series against South Africa.
Veteran wicketkeeper-batsman Dinesh Karthik and exciting fast bowler Umran Malik were picked for the five-match series beginning in New Delhi on June 9.
India's Test squad: Rohit Sharma (captain), KL Rahul, Shubman Gill, Virat Kohli, Shreyas Iyer, Hanuma Vihari, Cheteshwar Pujara, Rishabh Pant (wicketkeeper), KS Bharat (wicketkeeper), Ravindra Jadeja, Ravichandran Ashwin, Shardul Thakur, Mohammed Shami, Jasprit Bumrah, Mohammed Siraj, Umesh Yadav, Prasidh Krishna
India T20 squad: KL Rahul (captain), Ruturaj Gaikwad, Ishan Kishan, Deepak Hooda, Shreyas Iyer, Rishabh Pant, Dinesh Karthik, Hardik Pandya, Venkatesh Iyer, Yuzvendra Chahal, Kuldeep Yadav, Axar Patel, Ravi Bishnoi, Bhuvneshwar Kumar, Harshal Patel, Avesh Khan, Arshdeep Singh, Umran Malik.