Begay and the Oneida Indian Nation say a field of 12 will tee off Aug. 29 at the tribe's Atunyote Golf Club at Turning Stone Resort and Casino.
Other PGA Tour players scheduled to take part are K.J. Choi, Gary Woodland, Y.E. Yang, Charlie Wi and Danny Lee. LPGA Tour players signed up include Yani Tseng, Cristie Kerr, Lexi Thompson and Se Ri Pak.
Woods and Begay were roommates at Stanford.
The Challenge raises funds for Begay's charity, which fights obesity and diabetes among Native American children.