Shahbaz Sharif – the leader of an opposition coalition who worked to depose Mr Khan – is widely expected to win a majority of the votes.
The parliament is due to vote around 14:00 local time (09:00GMT).
Mr Khan, 69, was voted out after days of political drama and Supreme Court intervention.
He had attempted to block a previous attempt to bring a no-confidence motion against him by dissolving parliament and calling for a snap election.
However, the country’s Supreme Court upheld an opposition petition that his actions were unconstitutional and ordered the no-confidence vote to go ahead.
What do we know about Shahbaz Sharif?
Mr Sharif, 70, served as chief minister of Punjab, Pakistan’s most populous province, prior to Imran Khan coming to power in 2018. Mr Sharif, who leads the Pakistan Muslim League Nawaz (PMLN), had a reputation for efficiency and being hardworking, and is credited with making significant infrastructure improvements.
Many ruefully contrasted him with his successor, Usman Buzdar, who was widely ridiculed as under-qualified and incompetent. Anger at Imran Khan’s refusal to replace Mr Buzdar is one reason cited by numerous analysts for the emergence of a rift between Mr Khan and his previously close ally, the Pakistani military.
Shahbaz Sharif has always been in the shadow of his older brother, Nawaz Sharif, who served as PM on three occasions. Whereas Nawaz openly criticised the army following his removal from power, however, Shahbaz has favoured a reconciliation with the “establishment”.
Like his brother, Shahbaz has also faced corruption allegations and has spent periods of time in jail during Mr Khan’s tenure. He has not been convicted of an offence and maintains the allegations are politically motivated. Shahbaz Sharif’s son, Hamza, is hoping to follow in his father’s footsteps and become the next chief minister of Punjab.
Imran Khan’s supporters regard the Sharif clan as part of the dynastic, “old Pakistan” that they want to relegate to history.
Shahbaz Sharif submitted his candidacy for the top post on Sunday and is widely tipped to have the numbers to ensure victory.
Other opposition leaders – like Bilawal Bhutto Zardari of the Pakistan People’s Party (PPP) – have already indicated their support for him.
On Sunday, Mr Sharif heralded “a new dawn” for Pakistan following the vote.
However, Imran Khan, whose supporters protested across major cities after he was dismissed, is still blaming a “foreign conspiracy” for his removal as prime minister.
He has claimed, without evidence, that his rivals had colluded with the US to remove him because of his foreign policy stance on Afghanistan, Russia and China. Washington has strongly denied this. But the former international cricketer’s claims fed on anti-American sentiment held by many of his supporters.
He tweeted that the crowds seen were some of the largest in Pakistan’s history – a claim that has not been not independently verified.
How was Imran Khan ousted?
Mr Khan’s opponents saw an opportunity to strike after months of discontent over his management of the economy, and a breakdown in his relations with Pakistan’s powerful military.
Mr Sharif banded together with other opposition lawmakers to muster the numbers to vote Mr Khan out.
On 3 April, they challenged Mr Khan outright in parliament – launching a motion for a vote of no confidence in his leadership.
But the deputy speaker of the parliament – a political ally of Mr Khan’s – blocked the motion, claiming it was influenced by foreign powers. His government then swiftly dissolved parliament and called for a snap election.
The furious opposition immediately challenged the legality of government actions in the Supreme Court. After a four-day hearing, it ruled that Mr Khan’s government had acted illegally, in breach of the constitution.
Even then, Mr Khan and his party tried to prevent the vote in parliament for hours – with officials quitting, lawmakers filibustering and other disruptions.
But eventually, in the early hours of Sunday, his opponents secured his removal, with 174 lawmakers voting against him in the 342-member house.