Chief selector Inzamam-ul-Haq said that the squad has been selected after consulting head coach Mickey Arthur and captain Misbah ul Haq.
"The Test team has been selected keeping in mind the conditions in the West Indies and the recent performances of players during the domestic and international season," Inzamam said.
"The team is a fine blend of experience and youth and believe that team will do well on the tour," he said.
The series is expected to bring the curtain down on Misbah's career, having led the Test squad since late 2010.
Asghar and Shadab are yet to play Test cricket for Pakistan, although the latter has made an impressive international debut in the just-concluded T20 series, grabbing 10 wickets in the four-match series that Pakistan won 3-1.
Shah has been Pakistan's leading Test wicket-taker since late 2014.
Squad: Misbah-ul-Haq (capt), Sarfaraz Ahmad, Ahmad Shahzad, Azhar Ali, Shaan Masood, Babar Azam, Younis Khan, Asad Shafiq, Usman Salahuddin, Yasir Shah, Shadab Khan, Muhammad Asghar, Muhammad Aamir, Hassan Ali, Wahab Riaz, Muhammad Abbas.
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