Inzamam was banned for four one-dayers for bringing the game into disrepute at The Oval in August, when he led Pakistan's forfeiture of the fourth Test against England in protest at a ball-tampering penalty.
The first match of the series was washed out in Rawalpindi on Tuesday, but it counted as the fourth game that Inzamam missed.
"We have been told that Inzamam has completed the ban so he is back to lead the team," chief selector Wasim Bari told AFP on Tuesday.
Bari said Shoaib Akhtar and Mohammad Asif would also be considered for the remaining matches after the new-ball pair won their appeals against bans for doping on Tuesday.
Akhtar was banned for two years and Asif for one last month after they tested positive for the banned steroid nandrolone.
"We have announced the squad only for the second match because we will also consider the names of Akhtar and Asif for the next matches, as their bans have been overturned," said Bari, a former captain.
The third match will be played in Lahore (Dec 10) followed by the fourth at Multan (Dec 13) and the final game in Karachi (Dec 16).
Inzamam-ul-Haq (capt), Younis Khan vice-capt), Mohammad Hafeez, Imran Farhat, Yasir Hameed, Shoaib Malik, Mohammad Yousuf, Kamran Akmal (wk), Abdul Razzaq, Rao Iftikhar, Umar Gul, Mohammad Sami, Rana Naved-ul-Hasan, Danish Kaneria and Abdul Rehman.