The deal sending forward Speights and guards Ellington and Selby to the Cavaliers allows the Grizzlies to unload $6 million in salary and avoid paying a $4 million NBA luxury tax this season.
Under the transaction, Cleveland will obtain Memphis' first-round pick in the first available year.
"Marreese will strengthen our front court, while Wayne and Josh will add depth to our back court," Cavaliers General Manager Chris Grant said. "At the same time, we are adding a valuable asset with another future first-round pick, while also maintaining our future flexibility."
The deal came after it was learned Cavs center Anderson Varejao will miss the rest of the season with a blood clot in his lung.