White, a 6-foot-1, 175-pound guard, averaged 19.7 points, seven rebounds and 6.5 assists this season for Midland High, which qualified for the state playoffs and finished 24-7.
He garnered recruiting interest from New Orleans, Southern Methodist, and Texas A&M.
Ogden, a 6-foot-6, 190-pound shooting guard, attended Fork Union (Virginia) Academy and is one of seven NCAA Division I players on his team. He graduated from Seminole High in 2000 and is the younger brother of University of Texas junior forward Chris Ogden.
He drew recruiting interest from Kansas and several other smaller NCAA Division I schools.
Both players will enroll as freshman at Tech next fall. This season, freshman walk-ons Nathan Doudney and Ronald Ross both made starts for Tech.
Shropshire appeared in 24 games for Tech and averaged two points in 5.8 minutes per game this season.