Uber Technologies Inc. envisions taking to the skies with a fleet of food-delivery drones in as little as three years, an ambitious timeline for a ride-hailing company that would face numerous technical challenges and regulatory hurdles.

The San Francisco company is seeking an operations executive who can help make delivery drones functional as soon as next year and commercially operational in multiple markets by 2021, according to a job posting that appeared on Uber’s website. App-reliant Uber has limited experience developing hardware beyond its nascent electric scooters and its equipment for self-driving vehicles, an as-yet unproven technology.

The drone executive will “enable safe, legal, efficient and scalable flight operations,” according to the job listing, which refers to UberExpress, an internal name used for the drone delivery operation within its UberEats prepared-food delivery unit.

After an inquiry from The Wall Street Journal, Uber removed the job listing titled “Flight Standards and Training” from its site. A spokesman said the posting “does not fully reflect our program, which is still in very early days.”

Uber is crafting a narrative around its ambitions beyond ride-hailing, as it eyes a 2019 IPO that bankers say could value the company at $120 billion. It will have to woo investors who may be skeptical over its scandal-plagued past and lack of profits in the ride-hailing business by pointing to its plans for delivery drones, flying taxis and rental electric scooters and bicycles. Last week, it announced a new tractor-trailer rental business for long-haul truckers.

Proponents of unmanned aircraft such as Uber, Amazon.com Inc. and other companies are scrambling to draft wide-ranging blueprints for various home delivery efforts, ranging from training ground operators and certifying vehicles to analyzing hazardous incidents. But Uber sketched out a faster timeline than many regulators envision, and such companies generally have been careful to avoid antagonizing regulators by publicly laying out comprehensive plans before they have even been formally submitted or gone through vetting by regulators.

Uber Chief Executive Dara Khosrowshahi said at the company’s flying-taxi conference in May that it plans to run limited tests of food delivery by drone, but the job listing suggests the company is more serious about the initiative than previously believed. The company chose San Diego to test commercial drones in several U.S. cities as part of a federal program that includes firms like Alphabet Inc. and FedEx Corp.

“We need flying burgers,” said Mr. Khosrowshahi at the conference. He said deliveries within five to 30 minutes could be possible.

UberEats has been a bright spot for the company, according to Uber and its investors. It has expanded rapidly to hundreds of cities, and Mr. Khosrowshahi said this spring that its annual gross food sales—from which UberEats takes a commission—is growing at a rate that would reach $6 billion if stretched over 12 months. The unit dispatches drivers to restaurants to fetch orders arranged through Uber’s app.

Bankers hoping to help Uber with its IPO have valued UberEats at around $20 billion on its own, The Wall Street Journal reported earlier this month.

Before Uber can make any drone deliveries, the Federal Aviation Administration will have to develop rules for operating the vehicles beyond the sight of ground operators. Initial regulatory concepts aren’t likely to be revealed until the first quarter of next year, at the earliest, according to industry observers.

The agency also needs to develop additional rules for night flights and reliable drone identification while the vehicles are airborne. Adopting those rules could stretch into 2020, though Congress recently mandated a 2019 deadline for unveiling initial plans to permit package deliveries by drones.

Then there are the technical challenges. It can be difficult to accurately land the vehicles in a customer’s yard, and inclement weather can prevent the drones from taking off. The drones may be susceptible to vandalism or theft.

Other companies with drone-delivery ambitions have run into technical and other difficulties. In 2013, Amazon Chief Executive Jeff Bezos said the e-commerce giant could roll out viable delivery drones within four or five years. The company this year was snubbed by the U.S. Transportation Department’s testing program in which Uber is participating.

Alphabet in 2014 scrapped a drone design it had worked on for two years over technical concerns and in 2016 pushed out the leaders of its program. This summer it demonstrated one of its latest models making an ice cream delivery in Virginia in just a few minutes.

Uber, Amazon and other major drone champions are “effectively building a drone ecosystem” encompassing everything from airspace controls to pilot training standards, according to Joshua Ziering, co-founder of startup drone-services provider Kittyhawk.

“If companies don’t move on this now and it ends up happening quickly,” Mr. Ziering said, the laggards are likely to face immense difficulties catching up.

Write to Greg Bensinger at greg.bensinger@wsj.com and Andy Pasztor at andy.pasztor@wsj.com