Shahid Afridi will lead the T20 team while Azhar Ali will lead the ODI team in Zimbabwe.
The Test squad and the A team for the England series in the UAE starting from October 13 was also announced.
Misbahul Haq will lead the side against Cook's side in the UAE.
Pakistan will play two T20 matches with Zimbabwe on September 27 and 29, while three ODI matches will be played on October 01, 03 and 05.
Sohaib Maqsood made a comeback to the T20 and ODI squads after being out of the scene due to injury, while Wahab Riaz will also be available to represent Pakistan in all three formats after his recovery from hand injury.
Sarfraz Ahmed and Anwar Ali were not named in the T20 squad against Zimbabwe as the former was travelling to offer Hajj.
Veteran Test batsman Younus Khan and off-spinner Saeed Ajmal were excluded from the Zimbabwe tour, while the former made it to the Test squad against England.
"We have rewarded some outstanding performers in the recently concluded tournament and Imran was one of them," chief selector Haroon Rasheed said in a press release release.
Players have been directed to report to the training camp which will officially start from tomorrow, while they will travel for the Zimbabwe series on September 23.
T20 squad: Shahid Khan Afridi (C), Muhammad Hafeez, Ahmed Shahzad, Mukhtar Ahmad, Umar Akmal, Sohaib Maqsood, Shoaib Malik, Ahmer Yamin, Muhammad Irfan, Bilal Asif, Wahab Riaz, Imad Waseem, Sohail Tanveer, Muhammad Rizwan, Imran Khan Jr.
ODI squad: Azhar Ali (C), Muhammad Hafeez, Ahmed Shahzad, Sohaib Maqsood, Shoaib Malik, Babar Azam, Sarfraz Ahmed, Muhammad Rizwan, Imad Wasim, Anwar Ali, Wahab Riaz, Yasir Shah, Rahat Ali, Muhammad Irfan, Asad Shafiq.
Test squad for England series: Misbahul Haq (C), Ahmad Shahzad, Shan Masood, Azhar Ali, Muhammad Hafeez, Fawad Alam, Asad Shafiq, Younus Khan, Sarfraz Ahmed, Yasir Shah, Zulfiqar Babar, Wahab Riaz, Imran Khan, Rahat Ali, Junaid Khan.
A-Team to play practice matches against England in UAE: Junaid Khan (C), Sami Aslam, Khurram Manzoor, Fawad Alam, Umer Ameen, Ali Asad, Iftikhar Ahmed, Usman Salahuddin, Adnan Akmal, Muhammad Akhtar, Zafar Gohar, Ehsan Adil, Ziaul Haq, Ameer Hamza.
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