The ruling party Pakistan Muslim League-Nawaz (PML-N) named Mr Sharif's younger brother Shahbaz Sharif, who is the Chief Minister of Punjab, as his successor over the weekend, but he holds only a provincial seat, so must first enter parliament by contesting the seat left vacant by his elder sibling. 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 Mr 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 said.
Pakistan's opposition parties failed to agree on a joint candidate against PML-N's Shahid Khaqan Abbasi.
The PML-N enjoys a majority in the parliament so Shahbaz Sharif's ascension is expected to be smooth.
The publication of 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 Mr Sharif's four children -- daughter Maryam and sons Hasan and Hussein.
The court's ruling abruptly ended Mr 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 ousted before completing a full term.