Azam, Pakistan's biggest loser, sheds 30 kilos to earn cricket call-up
Khan, 22, has been on the radar of selectors for the last year, but was asked to trim his nearly 130-kilo weight before being considered.
"We have... recalled four experienced players and rewarded uncapped Azam for his domestic performance," said chief selector Mohammad Wasim.
Pakistan will play three ODIs and three Twenty20s against England in July, followed by five T20s and two Tests in the West Indies.
Medium-pace bowlers Mohammad Abbas and Naseem Shah were recalled for the Tests, while left-handed batsman Haris Sohail and all-rounder Imad Wasim regained their places in the white-ball squads.
Babar Azam will captain all three squads on both tours.
Pakistan will fly from Abu Dhabi on June 25 and play the first of three one-day internationals in Cardiff on July 8, after their mandatory quarantine.
ODIs: Babar Azam (capt), Shadab Khan, Abdullah Shafique, Faheem Ashraf, Fakhar Zaman, Haider Ali, Haris Rauf, Haris Sohail, Hasan Ali, Imam-ul-Haq, Mohammad Hasnain, Mohammad Nawaz, Mohammad Rizwan, Salman Ali Agha, Sarfaraz Ahmed, Saud Shakeel, Shaheen Shah Afridi, Usman Qadir
T20Is: Babar Azam (capt), Shadab Khan, Arshad Iqbal, Azam Khan, Faheem Ashraf, Fakhar Zaman, Haider Ali, Haris Rauf, Hasan Ali, Imad Wasim, Mohammad Hafeez, Mohammad Hasnain, Mohammad Nawaz, Mohammad Rizwan, Mohammad Wasim Junior, Sarfaraz Ahmed, Shaheen Shah Afridi, Sharjeel Khan, Usman Qadir
Tests: Babar Azam (capt), Mohammad Rizwan, Abdullah Shafique, Abid Ali, Azhar Ali, Faheem Ashraf, Fawad Alam, Haris Rauf, Hasan Ali, Imran Butt, Mohammad Abbas, Mohammad Nawaz, Naseem Shah, Nauman Ali, Sajid Khan, Sarfaraz Ahmed, Saud Shakeel, Shaheen Shah Afridi, Shahnawaz Dahani, Yasir Shah (subject to fitness), Zahid Mahmood