The Sixers also got forward Darius Songaila in Thursday's trade.
Brackins was taken by the Oklahoma City Thunder with the 21st overall pick in the NBA draft. He was then traded to New Orleans. Brackins averaged 16.5 points and 8.5 rebounds last season for Iowa State.
Songaila has averaged 7 points and 3.5 rebounds in seven seasons with Sacramento, Chicago, Washington and the Hornets.
Green played seven seasons with the Sixers, averaging 9.4 points in 422 games. Smith has also spent his entire career with the Sixers, averaging 4.0 points and 2.8 rebounds.