As many as 174 members voted in favour of the motion in the 342-member House while members of the ruling Pakistan Tehreek-e-Insaf were absent during the voting.
A special session of Pakistan Parliament will be convened on Friday to elect a new premier following Prime Minister Yousuf Raza Gilani's disqualification by the supreme court.
The Election Commission of Pakistan (ECP) on Tuesday publicly released the details of assets of key politicians, including that of Prime Minister Khan.
Mulk, 67, is likely to be sworn in on Friday, June 1.
Pakistani cleric Tahir-ul Qadri has announced to set up 'Awami Parliament' (People's Parliament) on Tuesday, as he refused to meet the PML-N government- appointed committee of lawmakers to hold talks with him.
Abbasi will be sworn-in in later at a special ceremony at the President's House.
Shaken by the Taliban terror attack in which 148 people, including 132 school children, were killed in Peshawar on Tuesday, Pakistan has pledged to announce a "national plan" to tackle terrorism within a week with Prime Minister Nawaz Sharif saying "this entire region" should be cleaned of terrorism.
Pakistan's powerful army chief has stepped in to mediate between the embattled government and the protesters seeking resignation of Prime Minister Nawaz Sharif, bringing the military back into the centre stage and signaling a possible end to the high-political drama.