The group, launched by FIFA president Sepp Blatter last month is being chaired by Jeffrey Webb, the president of CONCACAF, the confederation responsible for football in North and Central America and the Caribbean.
Premier League referee Howard Webb, Theo Van Seggelen, the head of the global players union FIFPro, Marcel Mathier, chairman of FIFA's disciplinary committee and Claudio Sulser, former chairman of FIFA's ethics committee, are also on the 12-man panel.
David Bernstein, the outgoing chairman of the FA, is included as is Piara Powar, the head of European anti-racism body FARE.
Blatter, announcing the Task Force when he visited Edinburgh last month, said there had to be stronger sanctions in force to tackle racism.
"We have seen that fines achieve little, but point deductions and exclusion from competitions could be more effective measures," he said.
UEFA General Secretary Gianni Infantino said earlier this month it was planning to introduce a minimum 10-game ban for anyone found guilty of racism and that clubs could be forced to close part or all of their stadiums if fans racially abused players.
Boateng, who plays for Ghana, 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 AZ Alkmaar in the Netherlands.
The Task Force will meet for the first time on May 6 and present its initial findings at the FIFA Congress in Mauritius at the end of May.