Deputies voted by 101 in favour and one abstention to approve the appointment, which speaker Murtuz Aleskerov said was a formal stepping stone to 41-year-old Ilham succeeding his father as president.
Under the Caucasus republic's constitution, the prime minister stands in for the head of state if he is incapacitated.
"The most worthy heir to the policies of Heidar Aliyev is Ilham Aliyev."
-Ali Ahmedov, ruling party deputy
Ilham Aliyev, who until now had been with his father in Turkey, was in the chamber for the vote. His appointment was followed by a standing ovation from deputies which lasted for several minutes.
"The most worthy heir to the policies of Heidar Aliyev is Ilham Aliyev," said Ali Ahmedov, a deputy with the Yeni Azerbaijan ruling party.
"His appointment as prime minister will let Azerbaijan flourish. All people loyal to Heidar Aliyev who have supported him for decades will now support Ilham Aliyev with the same enthusiasm."
Opposition parties boycotted the emergency session of parliament, but even if they had taken part they do not have enough seats in the chamber to have altered the outcome of Monday's vote.
There was no immediate word on the future of Artur Rasizade, the long-serving prime minister whom Ilham Aliyev replaces.