The official event is taking place in Ukraine's parliament.
Mr. Zelensky, who has no previous political experience, scored a landslide victory in last month's presidential election.
He ousted incumbent Petro Poroshenko who had been in power since 2014.
The newly elected president is taking the oath of allegiance to the Ukrainian people during the ceremonial meeting in parliament.
Mr. Zelensky has promised to tackle corruption and bring an end to the war with Russian-backed rebels in the east.
It is not clear which issues he will raise in his first speech as leader. The former television actor has said little since his resounding victory on 21 April.
There has been much political wrangling over the timing of Mr Zelensky's inauguration. He had wanted to hold it on Sunday, a day of mourning for victims of Stalin-era repression in the country.
But parliament disagreed and voted to hold it on Monday morning.
Who is Volodymyr Zelensky?
Mr. Zelensky starred in the long-running satirical drama Servant of the People in which his character accidentally becomes Ukraine's president.
He plays a teacher who is elected after his expletive-laden rant about corruption goes viral on social media.
He ran under a political party with the same name as his show.
With no previous political experience, Mr Zelensky's campaign focused on his difference from the other candidates rather than on any concrete policy ideas.
Despite this, he stormed to victory and won more than 70% of the vote.
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