The game will take place at Tuesday 30th July with a 7.30pm kick-off time at the Wings' Park View Road ground in the London Borough of Bexley.
The match will form part of the Development Squad's pre-season schedule, while there is also the potential for players from the First Team and Under-18s to be called into the squad if required.
Welling were crowned champions of the Conference South last season to take their place at the top level of English non-league football for the first time in 13 years.
Among the Wings' famous former players is ex-Saint Andy Townsend, who began his career with the south London outfit before going on to move to The Dell in 1985.
Their squad includes a number of players who began their careers with Premier League and Championship clubs. Defender Fraser Franks, for example, started out in the youth team at Chelsea, where he played alongside current Saints midfielder Jack Cork.
The Development Squad begins its pre-season friendly schedule next Tuesday, when Martin Hunter's side visits local outfit Sholing for a 7.30pm kick off.
Also on the agenda for the Under-21s this month are matches against Conference South side Eastleigh as well as their Brighton & Hove Albion counterparts.