The 20-year-old defender, pictured, featured for the Wings in their pre-season fixtures against Millwall's U21s and Greenwich Borough.
Nortey joined Chelsea at U15 level but left the Blues in 2013 at the end of his scholarship.
The right-back was a second-half substitute for manager Loui Fazakerley on Tuesday night when the Wings lost 1-0 at Forest Green Rovers.
Welling officials have not disclosed the length of his deal at Park View Road.