The claim is just the latest in a series of exciting pronouncements from the chief executive, who has repeatedly missed his own targets. But he has bet a considerable part of his business on the technology underpinning it.
As well as allowing for the robot taxis that will drive themselves around the streets, Mr Musk says that by next year there will be a million Tesla cars on the streets that have full autonomous technology and are able to drive themselves.
"Probably two years from now we'll make a car with no steering wheels or pedals," Musk predicted.
Central to this promise is a new microchip for self-driving vehicles unveiled by Musk on Monday during a webcast presentation. Made by Samsung Electronics Co Ltd in Texas, the chip now in all vehicles is hoped to give Tesla an edge over rivals and show its massive investment in autonomous driving - described by Musk as "basically our entire expense structure" - will pay off.
The webcast presentation came two days before Tesla is expected to announce a quarterly loss on fewer deliveries of its Model 3 sedan, which represents Tesla's attempt to become a volume car maker.
After launching the event with detailed technical descriptions of Tesla's progress on hardware and software by top executives, Musk began hawking the Model 3 and its potential.
"The fundamental message consumers should be taking away today is it's financially insane to buy something other than a Tesla. It's like buying a horse," saying Tesla was the only company to have a full self-driving suite of hardware.
Tesla's use of the term "full self-driving" garners criticism, as it sells such an option today that is not yet "Level 4," or fully autonomous by industry standards, in which the car can handle all aspects of driving in most circumstances with no human intervention. Musk has said that with the hardware complete, improvements in software will allow vehicles to fully drive themselves in future.
The technology faces many regulatory hurdles both in Washington and from local governments.
Global carmakers, large technology companies and startups are developing self-driving - including Alphabet Inc's Waymo and Uber Technologies Inc - but experts say it will be years before the systems are ready for prime time.
"A year from now we'll have over a million cars with full self-driving, software, everything," Musk predicted.
Tesla has been working on a self-driving chip since 2016 and Musk had previously forecast that cars would be fully self-driving by 2018, a target Tesla has missed.
Investors appeared unmoved by the chip announcement but shares rose slightly in after-hour trading following the announcement of the robotaxis.
Wedbush analyst Daniel Ives said Tesla's robotaxi ambition was "impressive," but added that investors will be concerned by "the practicality and financial implications of this endeavor especially with Waymo miles ahead of the autonomous competition."
More pressing for analysts, he said, were concerns about demand for the Model 3 and whether Tesla may seek new financing.
Musk took a swipe at competitors relying on Lidar, light-based sensors that are a key element in most other self-driving systems.
"Lidar is a fools' errand. And anyone relying on Lidar is doomed," said Musk, who has been vocal about the technology's limitations. Tesla vehicles rely on cameras and radars as their vision system for self-driving.
Competitors will eventually "dump" Lidar, he said: "It's expensive and unnecessary and once you solved vision it's worthless."
More than $1 billion in corporate and private investment has been plowed into some 50 Lidar startups over the past three years, including a record $420 million in 2018, according to a Reuters analysis of publicly available investment data in March.
Musk called Tesla's new chip the industry's best because it was dedicated for autonomous driving, while others, like Nvidia Corp, developed chips for multiple uses.
Tesla's chip was capable of seven times as many frames as Nvidia's Xavier system, said Pete Bannon, Tesla's head of Autopilot hardware. Nvidia said the comparison was inaccurate.
U.S. magazine Consumer Reports cautioned against Tesla's "bold claims about self-driving capabilities that overpromise and underdeliver."
"Claims about (Tesla's) driving automation systems and safety are not backed up by the data, and it seems today's presentations had more to do with investors than consumers' safety," wrote the publication.
Additional reporting by Reuters