In a televised address, Oxford-educated Khan claimed victory, as his Pakistan Tehreek-i-Insaf (PTI), or Pakistan Movement for Justice, was in a commanding lead, the country’s election commission said.
About half of the votes from Wednesday’s election have been officially declared.
His success marks an epic rise for the anti-corruption crusader who has spent most of his political career on the fringes of Pakistani politics.
However, the count has been marred by accusations of corruption and rigging by all other major parties.
This has been exacerbated by the lengthy vote-count, which was due to be completed by 10pm BST on Wednesday (2am local time on Thursday).
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Now nearing the 24-hour mark, the count continues, but the Election Commission of Pakistan (ECP) secretary Babar Yaqoob told reporters that counting had been delayed by technical failures in an electronic reporting system and the tallying was now being conducted manually.
He said: “There’s no conspiracy, nor any pressure in delay of the results. The delay is being caused because the result transmission system has collapsed.”
Meanwhile, supporters of Khan, 65, have begun celebrating what seems a sure victory, though we will need to wait for the final count to see if PTI will win a simple majority or need to form a coalition government.
His speech, from his home near Islamabad, has inspired confidence.
He said: “God has given me a chance to come to power to implement that ideology which I started 22 years ago.”
He promised to create jobs for the poor and announced he would turn the palatial prime minister’s official residence in the capital into an education facility instead of living in it.
Khan offered to investigate all the claims of rigging and said he wants to “unite” the country under his leadership.
“Accountability will start with me, then my ministers, and then we will work our way down,” Khan said.
“I want all of Pakistan to be united in this moment.”
In his populist pledge, he called for improved relations with the US and India, and called for better trade ties to reduce poverty.
During his campaign, he promised an “Islamic welfare state” and cast his populist campaign as a battle to topple a political elite.
Yet corruption allegations plagued the run-up to the election, with allegations of pro-Kahn military meddling rife, right up until the vote count.
Khan has staunchly denied allegations by incumbent party, Pakistan Muslim League-Nawaz (PML-N) that he is getting help from the military, which has ruled Pakistan for about half of its history and still sets key security and foreign policy.
The army has dismissed the allegations.
Final vote counts are expected later tonight.
Follow our live updates as the counts come in here.