Mr Abassi's tenure is expected to be short as Nawaz Sharif has chosen his brother Shahbaz Sharif as the successor once he becomes eligible.
The country's ruling Pakistan Muslim League-Nawaz (PML-N) had named Nawaz Sharif's younger brother, who is the Chief Minister of Punjab, as his successor over the weekend. But Shahbaz Sharif holds only a provincial seat, so he must first enter parliament by contesting the seat left vacant by his older brother. He will also have to resign as member of the state legislative of Punjab and a new Chief Minister will have been identified.
In the meantime the party has nominated Mr Abbasi as interim Prime Minister. The 58-year-old loyalist of Nawaz Sharif will hold the PM's office for a period of 45 days and will resign to let Shahbaz Sharif succeed as permanent PM, party sources say.
Pakistan's opposition parties failed to agree on a joint candidate against PML-N's Shahid Khaqan Abbasi.
The 11.5 million secret documents from Panamanian law firm Mossack Fonseca documenting the offshore dealings of many of the world's rich and powerful implicated three of Nawaz Sharif's four children -- daughter Maryam and sons Hasan and Hussein.
The court's ruling abruptly ended Nawaz Sharif's third tenure as Prime Minister and forced the party's top leadership to find his successor.
Nawaz Sharif was the 15th Prime Minister in Pakistan's 70-year history -- roughly half of which was under military rule -- to be removed before term.