The trial will use a small two-seat vehicle called the Fetch, developed by British company Imperium Drive.
Users can order a car through a smartphone app.
"It's driverless but not autonomous," said Imperium Drive CEO Koosha Kaveh. "There's still a human involved, but they will be sitting in a control centre controlling the vehicle in the same way you would control a drone.
"We're working towards making remote driving safer than normal driving. In normal driving, you still have blindspots around you that cause accidents. You also can't anticipate what's coming in terms of traffic, pedestrians or cyclists.”
Each Fetch makes use of technology that can detect its surroundings, improving safety.
The vehicles have already been in use in car parks and on private land around the town, but the next step of the trial will involve players and staff of Milton Keynes Dons Football Club.
The cars are said to be helpful in preventing the spread of Covid-19, which has continued to affect the world of sport over the past few months.
"Our players and staff can now order a vehicle through the app that will arrive at the front of the stadium to take them to training,” said MK Dons’ performance director, Simon Crampton.
"The biggest thing at the moment is Covid, because we can't start putting players together in cars, particularly with the Omicron variant being very contagious."
The trial has the support of both the UK government and Milton Keynes Council, which hopes the town will move towards car-sharing and driverless technology in the next two years.
"We've been working at this for a number of years. We want people to move away from single occupancy cars,” said the council’s head of transport innovation, Brian Matthews.
"We're looking for a range of solutions – not just these driverless cars but also larger shuttles using similar technology and four-seater pods that are completely autonomous."
The trial on public roads will start towards the end of January.