The Bulls acquired Thomas from the Knicks before the 2005 season, but he only played three games with them. Chicago sent him home that December and waived him in March.
On Wednesday, the Bulls sent forward Andres Nocioni, center Drew Gooden and reserves Cedric Simmons and Michael Ruffin to Sacramento for center Brad Miller and swingman John Salmons.
The Knicks also traded for Chris Wilcox, the veteran Oklahoma City forward who had been involved in the Thunder's deal for Tyson Chandler that was later rescinded.
Oklahoma City gets seldom-used forward Malik Rose in the deal. Both players have contracts that run out at the end of the season.
Wilcox had been receiving limited playing time since the Thunder signed restricted free agent Nenad Krstic in late December, and returning to Oklahoma City after the first trade was voided didn't figure to sit well with the seventh-year player.
He and Joe Smith were to be traded to the Hornets, along with second-round pick DeVon Hardin.
Rose had also been spending most of his time on the bench. He played in only three games with the Knicks since late December and was averaging less than two points and two rebounds this season.