WASHINGTON—Hours after comedian Volodymyr Zelensky won a landslide victory in Ukraine’s April presidential election, President Trump was on the phone hailing his success.

The first call was “very brief,” and aimed mostly at offering introductory pleasantries, according to two officials with direct knowledge. Mr. Trump also encouraged Ukraine’s president-elect to follow through on his commitments to tackle corruption, these people said. The White House didn’t immediately respond to a request for comment.

Mr....