President Mamnoon Hussain administering oath in a ceremony held in Islamabad.
Naeem Lodhi is a former defence secretary whereas Rehman is well-known figure among trade circles.
Caretaker Prime Minister Nasirul Mulk, members of the federal cabinet and other senior officials attended the ceremony.
A six-member caretaker federal cabinet was sworn in earlier this month. The caretaker cabinet includes the State Bank of Pakistan's former governor Dr Shamshad Akhtar, Roshan Khurshid, Barrister Ali Zafar, former ambassador to the United Nations Abdullah Hussain Haroon, Azam Khan and Muhammad Yusuf Shaikh