Left-handed opener Ayub made a strong impression in the Pakistan Cup, where he finished as the tournament's highest run-scorer.
Right-arm fast bowler Shahzad was the highest wicket-taker in Pakistan's premier domestic first-class tournament, the Quaid-e-Azam Trophy, this season.
Faheem Ashraf, Mir Hamza and Mohammad Wasim Jr were all recalled to the squad.
Shan Masood will lead the team for the first time after taking over the role from Babar Azam.
"The squad has been assembled keeping in mind the challenging Australian conditions," Pakistan's new chief selector Wahab Riaz said on Monday.
"We have kept the pitches in mind and added more pace bowling resources to the team to ensure that the management can be flexible with the team combinations in all three test matches."
The first Test starts in Perth on December 14th.
Pakistan squad:
Shan Masood (captain), Aamir Jamal, Abdullah Shafique, Abrar Ahmed, Babar Azam, Faheem Ashraf, Hasan Ali, Imam-ul-Haq, Khurram Shahzad, Mir Hamza, Mohammad Rizwan, Mohammad Wasim Jnr, Noman Ali, Saim Ayub, Salman Ali Agha, Sarfaraz Ahmed, Saud Shakeel and Shaheen Shah Afridi.