Zelenskyy is expected to try to convince Biden to change his mind.
“We have arrived in the United States of America,” Zelenskyy said on social media.
“The plan for Ukraine’s victory will be on the table for all our allies.”
He said he was starting the trip in Pennsylvania for a “special visit” – without giving details – before travelling to New York and Washington.
Zelenskyy said the coming weeks would decide how more than 30 months of fighting that has killed thousands would end, calling on world leaders to think of their legacies.
“It is now being determined what the legacy of the current generation of state leaders will be. Those in the highest offices,” he said.
In comments before his trip, Zelenskyy said the United States and the UK have not given Ukraine permission to use the long-range weapons as they fear escalation, but hinted he had not given up hope Biden would make a U-turn.
“We have had some decisions in the history of our relationship with Biden – very interesting and difficult dialogues,” Zelenskyy said earlier this week, adding: “He later changed his point of view”.
Moscow has said it considers such a go-ahead as NATO countries being “at war” with Russia.
