Dallas and Los Angeles in the USA will also be pilot cities.
According to Susan Anderson, Regional General Manager for Uber in Australia, New Zealand and North Asia, Australian governments have adopted a "forward-looking approach to ridesharing and future transport technology" - making the ground-breaking trial possible.
"As major cities grow, the heavy reliance on private vehicle ownership will not be sustainable", said Eric Allison, global head of the firm's aviation division Uber Elevate.
"India presents challenges with respect to the way we are actually able to operationalise Uber Air in the country and we had some discussions with the aviation authority and several of the state government representatives and it looks promising", added Allison. The 19km journey from the central business district to the airport is expected to take 10 minutes by air, compared with the 25 minutes it usually takes by auto.
Test flights are expected in 2020, with commercial operations aimed for as soon as 2023.
"We are delighted that Melbourne has been chosen as the first global trial city for Uber Air".
The announcement was made at the company's Elevate summit in Washington after sealing the deal with Melbourne Airport and companies Macquarie Capital, Scentre Group and Telstra.
The lawsuit was filed at the Victorian Supreme Court by law firm Maurice Blackburn Lawyers, and will cover more than 6,000 drivers, operators, and licence owners across Victoria, New South Wales, Queensland, and Western Australia, making it one of the biggest class actions in Australian history.
Uber Air's drone-like "flying taxi" uses vertical take-off and landing.
One of Uber Air's Skyports.
It would not be the first time Uber has offered an air service in Melbourne.
Uber has proposed using vehicle park roofs - including those of shopping centres - and existing helipads to run the service.
It had taken the state almost three years to decide how to legislate ride-hailing services such as Uber, announcing back in September 2015 that it was preparing to regulate the service amid concerns from the local taxi industry.
A large part of Uber's plan to take to the skies involves the development of electric helicopterlike aircraft that will be both ecologically friendly and significantly quieter than traditional helicopters, both due to their lack of noisy turbine engines and because they will use multiple smaller rotors to provide lift, rather than a single large one.
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