Eight of the new vehicles will start running a busy city route from the end of January and will run 17 hours a day, seven days a week, carrying 800,000 passengers a year.
The project is a trial designed to demonstrate electric vehicles can run just as long and just as well as traditional diesel powered buses.
The technology relies on a process called inductive charging in which electricity passes through wire coils in plates on the road creating a magnetic field.
This induces a charge in secondary coils in plates attached to the underside of the bus, charging the vehicles batteries.
The technology is already used in a system in South Korea.
The head of service delivery at Arriva, Maq Alibhai, told MKNews: "For customers the journey on Route 7 from Wolverton to Bletchley, which the electric bus will be trailing on, will be much smoother and noise reduction will be another main benefit.
"With the new technology the buses will be charged at the depots over night and will use the inductive charges that will give them more charge at certain stops throughout the day when they pick up passengers."
Because the busses are charged as they travel they can carry lighter batteries which in turn require less energy to transport.
The buses have been built by UK bus manufacturer Wrightbus.