This is his first international trip since Russia invaded Ukraine in February.
Zelensky would address Congress and take part in other events while in the US, according to Prime9jaOnline.
The White House has approved the idea, and the US will provide Ukraine a Patriot missile battery to strengthen its air defences.
"On my way to the US to strengthen Ukraine's resilience and defence capabilities," he tweeted on Twitter.
At his residence in Kyiv, Zelensky often hosts guests from other countries, and he has visited Ukrainian soldiers all around the nation.
Numerous phone and video conversations have been made by the president of Ukraine to other world leaders, frequently from his office in Kiev.
His unexpected overseas journey is the first of its type since hostilities began. It conveys a clear statement on the importance of Ukraine's relationship with the US, which has been instrumental in providing military support.
In a briefing before to Zelensky's visit, the White House reaffirmed the roughly $2 billion (£1.6 billion) in fresh security assistance for Ukraine. One of the aids offered is a brand-new Patriot.