Wearing a Make America Great Again hat "made me feel like Superman", he said.
West had been invited to the White House for lunch to discuss prison reform and other issues.
At the end of the 10-minute monologue, during which Mr Trump nodded in approval, the president said: "That was quite something."
West replied: "It was from the soul. I just channelled it."
"I love this guy right here," West said, walking behind the desk to hug the seated president, who said: "That's really nice."