The test uses a sample of blood taken in a heel prick shortly after birth.
Nelson said: “After years of campaigning, it means so much.
“Today is a day of hope. Knowing that future families will have access to early diagnosis and the opportunity for the best possible outcomes is something I’m incredibly proud to have supported.
“This is a victory for every family affected by SMA. Whilst it can’t change the future of our children, I know it marks the beginning of a brighter future for future SMA families.”
Hundreds of thousands of babies are expected to be screened for SMA as part of the study, which will be led by scientists at the University of Oxford.
That will help the UK National Screening Committee make a final decision on whether SMA testing should become a permanent fixture.
James Murray, the health secretary, said he was “in awe” of campaigners who had worked to raise awareness of SMA.
“No parent should have to watch their child lose the ability to move or breathe, knowing that earlier treatment could have made all the difference,” Murray said.