Uber Technologies Inc. has selected the New York Stock Exchange for its imminent initial public offering, handing the trading floor what could be one of the five biggest listings of all time, according to a person familiar with the matter, who asked not to be identified as the details aren’t public.

The ride-hailing giant is expected to publicly file for its offering in April, kicking off a listing that could value the company at as much as $120 billion and is likely to be the biggest of the year, people familiar with the plans have said previously. At that valuation,...