The system, now being tested in Britain, works by re-routing sounds from the deaf ear to the working one.
Standard hearing aid devices often don't work for people with single-sided hearing loss because their inner ear or nerves are too badly damaged.
The new hearing aid, called the SoundBite, uses the bones of the head to conduct the sound to the working ear, the Daily Mail reported.
When sound waves enter the ear, they travel to the eardrum and make it vibrate. These vibrations then go to the inner ear, which contains around 20,000 tiny hair cells.
These cells move in response to the vibrations, and this movement is converted into electrical impulses that are sent along nerves to the brain, which interprets them as sounds.
With standard hearing aids, an external microphone picks up the sound, amplifies it and delivers into the ear.
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The SoundBite consists of a tiny microphone, placed just inside the ear canal of the impaired ear to capture the sound travelling into the ear.
These sounds are then sent to a small transmitter, worn behind the ear (and smaller than a conventional hearing aid), which transmits them to a device in the mouth.
This device is roughly the size of half a matchstick and loops over the patient's left or right back teeth, a bit like a wire for a dental plate.
Once it receives a sound transmission, the tooth device converts these signals into tiny vibrations, which are imperceptible to the user.
The vibrations are conducted via the teeth, through bone, to the working ear, where the sound vibrations are turned into nerve impulses, and sent to the brain.
Some types of hearing aid already use bone conduction, known as bone-anchored hearing aids. With these devices, a small titanium plate is inserted into the back of the skull, behind the ear.
The plate detects sound vibrations, and sends these through the skull. However, these need to be surgically fitted, and are visible on the outside of the head.
A study published in the journal Otology & Neurotology showed that the new device improved the ability of patients to understand speech in noisy environments by an average of 25 per cent, and that for one third of the patients, the improvement exceeded 30 per cent.
A year-long trial of the device, which costs around 600 pounds, is now under way at various centres across Europe, including University Hospital Southampton.