Several supporters draped themselves in the Tricolour and flashed victory signs as the giant screen showed the party's surge.
The party workers interpreted the AAP show as the victory of development works.
"Delhi bach gaya," said 21-year-old Ramesh Sharma, an engineer and a volunteer who has been campaigning for the party for the past three months.
"We have barely slept in the last few months. I can't tell you how happy we are. It has sent a very strong message that only development work talks, nothing else," he said.
A stage, decorated with balloons and flowers, was also set up on the roof of the party office, from where Kejriwal is expected to address workers after the final results are announced.
Accompanied by his political strategist Prashant Kishor and senior party leaders Gopal Rai and Sanjay Singh, the chief minister was at the party office, following trends but did not come out.
According to the Election Commission (EC), the ruling Aam Aadmi Party is leading on 59 seats while the BJP on ahead in 11.
"We knew it. We have changed the politics of this country. Now it is Delhi, next is India," said a jubilant Sanjeev Singh, a party volunteer from Hari Nagar.
"We hope we get such a clear majority that a message goes out that doing Hindu-Muslim politics will not work anymore," added another volunteer Fareen Khan.
The AAP headquarters were decorated with blue and white balloons and big cut-out of Kejriwal was also put up.
A big poster saying "Acche honge paanch saal, Delhi mein toh Kejriwal" was also put up. AAP Rajya Sabha MP Sanjay Singh dedicated the victory to the people of Delhi.
"Hindustan jeeta hai (India has won). I want to thank the two crore people of Delhi for making the son of Delhi victorious," Singh said.
"People of Delhi have showed the way to the country that only development works will take it forward and not Hindu-Muslim politics. All kind of divisive politics has been rejected by the people of Delhi and we will win 70 out of 70 seats," said Sushil Gupta, AAP Rajya Sabha MP.
According to the Election Commission website, AAP convenor Kejriwal is leading in his New Delhi constituency.
Counting centres are spread across 21 locations, spanning 70 constituencies.
Polling for the 70-member Delhi Assembly was held on Saturday.
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