Anthony, a 10-time All-Star, will not play a game for the Bulls, who will eventually trade or waive him before the Feb. 7 trade deadline, league sources told ESPN.
In addition to Anthony, the Bulls received the draft rights to Jon Diebler. Houston received the draft rights to Tadija Dragicevic.
The teams wanted to complete the deal Monday, but the league office was closed for Martin Luther King Jr. Day and a trade call couldn't be executed to finalize the deal, sources said.
"I don't think it's right," Rockets coach Mike D'Antoni said of having to terminate Nunnally. "There's ways [the league] could have facilitated it."
League office staff are available to take trades during holidays, but teams must notify the league office of the terms of the possible trade by 6 p.m. ET on the business day prior to the holiday, the league has told teams previously. The league has similar rules for deals agreed upon over weekends. The NBA says the rule is designed to make sure that trades are in compliance and that all teams have an equal chance to complete deals on weekends.
The Bulls will not immediately waive Anthony and could use him in a one-for-one trade before the trade deadline, sources said. For Anthony, this gives him the freedom to survey the league's roster landscape post-trade deadline and find the best fit for him.
The Los Angeles Lakers have an interest in Anthony but have no plans to waive a player to create an available roster spot for him, league sources said. If a roster spot becomes available with the Lakers before or after the trade deadline, L.A. will be a possible destination for Anthony, league sources said.