Mr Trump said at a news conference after a face-to-face meeting with Mr Kim that “real change is indeed possible”.
He also said that he is prepared “to start a new history” and “write a new chapter” between the two nations.
He said: “The past does not have to define the future.”
Mr Trump and Mr Kim concluded the extraordinary summit by signing a joint document in which they committed to working towards the “complete denuclearisation of the Korean Peninsula”.
The document signed by the two leaders also said they will join efforts “to build a lasting and stable peace regime” on the Korean Peninsula.