UCLA ends its season having won 13 of its last 17 games following a 69-61 loss to No. 2 seed UConn in the NCAA Tournament Regionals in Albany, New York.
The roster that began with 35 hopefuls was trimmed down to 12 following three days of trials.
Burke scored 11 points on 4-for-10 shooting.
Onyenwere is one of seven athletes selected from the Pac-12 Conference.
Onyenwnere is one of eight athletes who submitted applications and were accepted by USA Basketball to compete in the tournament.
In four seasons, Burke registered 1,513 career points, 657 rebounds, 258 assists, 237 steals, and 123 blocks.