Outgoing FA chairman Bernstein and Premier League referee Webb will join AC Milan and Ghana midfielder Kevin-Prince Boateng and former Hull City and United States striker Jozy Altidore on the 12-man panel.
The group is being chaired by CONCACAF president Jeffrey Webb and also includes Marcel Mathier, the chairman of FIFA's disciplinary committee and Claudio Sulser, the former chairman of FIFA's ethics committee and Piara Powar, the head of European anti-racism body FARE.
The Task Force will meet for the first time on 6 May and present its initial findings at the FIFA Congress in Mauritius at the end of the month.
Both Boateng and Altidore have experienced racism while playing.
Boateng led his AC Milan team off the field after being racially abused by fans of Pro Patria, an Italian fourth division club, in a friendly in January.
Altidore was racially abused while playing for current club AZ Alkmaar in the Netherlands.