Training camp will take place Sept. 17-19 at the University of Miami.
Burke made seven starts as a rookie and averaged 4.4 points, 1.5 rebounds and 0.7 assists per game.
Onyenwere and Team USA will begin pool play on Friday against the Netherlands at 2:20 p.m. (PT).
Nyingifa averaged 6.2 points per game during Nigeria's championship run.
Onyenwere averaged 12.7 points and 9.0 rebounds in three wins for USA.
UCLA will open Pac-12 play by hosting crosstown rival USC during the weekend of Dec. 27-29.