The Sixers announced the deal on Saturday.
White was a first-round pick (16th overall) last summer and never played for the Rockets. The 6-foot-8 White was on the inactive list as he worked on an arrangement with the team to balance his acknowledged anxiety disorder with the demands of the NBA schedule.
White was vocal on Twitter throughout the saga, often criticizing the team. The Rockets suspended White on Jan. 6 after he refused to accept an assignment to Rio Grande Valley in the NBDL.
Aldemir was the 53rd overall pick by the L.A. Clippers in the 2012 NBA draft. His rights were traded to Houston that night as part of a four-team deal that also involved Dallas and Utah.