Uber Technologies Inc.’s new chief executive, Dara Khosrowshahi, said he would start on Tuesday and aim for an initial public offering in as soon as 2019, setting the stage for what would be one of the most highly anticipated market debuts in memory.

At his first appearance in front of employees for the ride-hailing firm Wednesday, Mr. Khosrowshahi set a timeline for an IPO of between 18 and 36 months, though he indicated that wasn’t a firm deadline, according to a person who attended the meeting. The wide range gives Mr....