After learning that Randolph with miss six to eight weeks with a torn medial collateral ligament, suffered Sunday in Chicago, the Grizzlies on Wednesday completed a three-team trade with Philadelphia and New Orleans.
The deal sends Memphis swingman Xavier Henry to the Hornets.
Completing the transaction are two second-round picks to the 76ers: The Hornets will send theirs from 2013, and the Grizzlies send theirs from 2012.
Philadelphia general manager Rod Thorn said trading "will give us additional assets moving forward, including a trade exception, which will help us as we look to continue to improve our team."
Teams with a trade exception have up to a year in which they can acquire more salary in other trades than they send away.
The Grizzlies were in search of added depth in the frontcourt even before Randolph was injured, having already lost versatile forward Darrell Arthur, their most valued reserve, to a season-ending Achilles injury last month.
On Wednesday, the team announced that Randolph's MRI revealed the ligament tear. He was injured when teammate O.J. Mayo fell onto him in during a 40-point loss in Chicago.
Memphis wanted to move quickly in the wake of its 2-3 start. The Grizzlies have never faced higher expectations after upsetting top-seeded San Antonio in the first round of last season's playoffs before losing to Oklahoma City in the second round in seven games.
Randolph averaged 20.1 points and 12.2 rebounds last season and was averaging 19 points and nine rebounds before he was injured.
Speights, 6-foot-11 and 245 pounds, is in his fourth season with the 76ers, who selected him out of Florida with the 16th overall pick in the 2007 draft but has never averaged more than 16.4 minutes per game in the NBA. He has not played this season.
Henry, 6-6 and 220 pounds, played in 38 games as a rookie last season in Memphis but has missed the start of this season with torn ligaments in his right ankle.
"We are delighted to welcome Xavier to our team and the New
Orleans community," Hornets general manager Dell Demps said in a
release Wednesday. "We hope Xavier will develop into a good
basketball player that will contribute to the success of the New
Orleans Hornets this season and into the future."
Marc Stein is a senior NBA writer for ESPN.com. Information from The Associated Press contributed to this report.