Shahbaz Sharif, the current chief minister of Punjab province, must first enter parliament by contesting the seat left vacant by his elder sibling.
The National Assembly speaker Sardar Ayaz Sadiq opened the parliament session on Tuesday afternoon for the vote, with an oath-taking scheduled for the new prime minister by evening.
Pakistan's constitution requires a candidate for prime minister to win a majority from the National Assembly, the lower house of parliament.
Three opposition candidates also submitted nomination papers to take part in the vote.
Cricketer-turned-politician Imran Khan and his opposition Pakistan Tehreek-e-Insaf (PTI) party, who led the campaign against Nawaz Sharif, have nominated Awami Muslim League head Sheikh Rashid Ahmed as their candidate.
But Abbasi, a long-time Sharif loyalist, is expected to win the vote easily as the PML-N commands a majority in the 342-member assembly.
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.
The top court ousted Sharif Friday after an investigation into corruption allegations against him and his family, bringing his historic third term in power to an unceremonious end and briefly plunging the nuclear-armed nation into political instability.
Abbasi is the former federal minister for petroleum and natural resources, and a businessman who launched the country's most successful private airline, Air Blue.
Educated in the US at George Washington University, he worked in the US and Saudi Arabia as an electrical engineer before joining politics and being elected to the National Assembly six times.
He was arrested after the military coup led by General Pervez Musharraf which ended Nawaz Sharif's second term as PM, and imprisoned for two years before being released.
Shahbaz Sharif, considered more brainy than his charismatic older brother, went into exile in Saudi Arabia along with Nawaz after Musharraf's coup.
He returned to Pakistan in 2007 and was elected chief minister in the family's power base of Punjab in 2008, becoming the longest serving top official in the province.
A tough administrator with a reputation for passionate outbursts and a fondness for hats, he is known for using revolutionary poetry in speeches and public meetings and considered by some to be a workaholic.
His scandalous relationships fuelled headlines in the past, but his marriage to the author Tehmina Durrani, who is his fifth wife, in 2003 has since dampened the media frenzy.
Shahbaz Sharif has been so far largely unscathed by the claims about the lavish lifestyles and luxury London property portfolio of the Sharif dynasty which have played out for months in the country's raucous news media.
It was an investigation into the claims, which first erupted with the Panama Papers leak last year, that eventually saw the Supreme Court oust Nawaz Sharif. Sharif's family has denied the accusations.
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