Zelensky said Trump confirmed the move during their meeting this week on the sidelines of the UN General Assembly in New York.
"President Trump told me: yes, I have made the final decision. Ukraine will receive a licence to produce Patriot missiles", Zelensky said in a voice message to reporters.
Kyiv has pushed for years to build its own interceptor missiles, arguing they are vital to defending against Russian ballistic missile attacks.
Trump first floated the idea at the NATO summit in Ankara earlier this year, telling Zelensky: "We'll show them how to do it", the American leader said.
He later appeared to hedge. At a government meeting in late July, Trump said no agreement had been reached, citing the risks of transferring sensitive technology.
Zelensky said Tuesday that teams from both countries were already working to get Ukrainian Patriot production running.
(jh)
Source: Euronews