The terms of the deal have not been disclosed.
"But this deal will certainly help in terms of marketing and potentially attract further investors to come into the operation."
Hyperloop One recently tested a prototype pod in the Nevada desert, which reached a speed of 310km/h (192mph) within a 500m (1,600ft) low air-pressured tube.
Its eventual goal is to reach 1,046km/h (650mph).
The system uses magnetic levitation and electric propulsion to cause pods to glide, and is pitched as a more eco-friendly mode of transportation than many of today's alternatives.
The firm says it is working on several projects to bring the technology to the Middle East, Europe, India, Canada and the US.In a press release, Virgin suggested the system could eventually cut journey times from Edinburgh to London to 50 minutes.
Hyperloop's inventor, Elon Musk, has previously signalled his intention to build a separate Hyperloop system via his tunnel-digging Boring Company.
Hyperloop Transportation Technologies, TransPod Hyperloop and Dinclix GroundWorks are among other companies to have announced rival projects.
'Complicated tech'
"The combination of our proven technology and Virgin's expertise in transportation, operations, safety and passenger experience will accelerate the commercialisation phase of our company's development," said Hyperloop One's co-founder Josh Giegel in a written statement.
Virgin already has investments in rail companies, cruise liners, airlines and a nascent space tourism operation.
However, Prof Bailey questioned its potential.
"I remain sceptical about using Hyperloop technology in places where there are high land values or dense population," he explained.
"But it may be more appropriate in places like the United Arab Emirates.
"It's a complicated technology and there's a long way to go."