Experts say the device, which is placed below the injury, helps lost signals from the brain reach the leg muscles.
US research teams at the University of Louisville and the Mayo Clinic, report the success in Nature Medicine and the New England Journal of Medicine.
One of the recipients says her life has been transformed by the technology.
Kelly Thomas, 23, from Florida, is one of two patients at the University of Louisville who has been helped by the development, which has been combined with months of intense rehabilitation therapy.
She said: "Being a participant in this study truly changed my life, as it has provided me with a hope that I didn't think was possible after my car accident.
"The first day I took steps on my own was an emotional milestone in my recovery that I'll never forget, as one minute I was walking with the trainer's assistance and while they stopped, I continued walking on my own. It's amazing what the human body can accomplish with help from research and technology."
Jeff Marquis, who was injured in a mountain-biking accident, has also benefited.
The 35-year-old is now able to walk for himself with support either from a frame or from people on either side of him holding his hands.
A third patient, 29-year-old Jered Chinnock, was treated at the Mayo Clinic in collaboration with the University of California, Los Angeles.
He injured his spine in 2013 in a snowmobile accident. Since having the patch fitted he has been able to walk more than 100m with the support of a frame.