The wicketkeeper-batsman has replaced Shahid Afridi, who stepped down from the position after Pakistan lost three of their four group matches at the recent ICC World Twenty20.
"I spoke to Sarfraz this morning and conveyed to him that he was our natural choice for this position," the Pakistan Cricket Board's chairman Shaharyar Khan said in a statement.
"His appointment is open-ended. I wish him good luck in his new role."
Twenty-eight-year-old Ahmed has made 21 T20I appearances, from which he has scored 291 runs.