Trump, emerging from the elevators of his Trump Tower with West by his side, called the rapper a "good man" and told journalists that they have been "friends for a long time".
When asked what did the two discuss during their meeting, Trump said "Life, we discussed life".
West's appearance at the Trump Towers came only days after the rapper first came back into the public eye following his hospitalisation.
West, who had declared last year that he would run for President in 2020, remained mostly silent and did not comment when asked whether he plans on performing at Trump's inauguration. He also ignored a question about whether he wishes he had voted for Trump.
"You take care of yourself, I'll see you soon," Trump told West.
West had asked for a 15-minute meeting with Trump, transition spokeswoman Hope Hicks said.
It was not clear why TV reality star Kim Kardashian's husband met Trump. West walked in with a slight smile and made his way to the elevator. He was accompanied by an entourage that included a videographer.
West had been hospitalised last month due to exhaustion. He had abruptly ended a concert in California, saying had he voted, he would have voted for Donald Trump.
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