Rose had six points and 11 assists.
Rose hurt his wrist and elbow at the end of Monday night's game against the Indiana Pacers at the United Center. X-rays on the wrist after the game were negative.
"They're both going [to play Wednesday]," Thibodeau said of Rose and Noah. "They went through shootaround no problems so they're going."
Rose, who is averaging 24.7 points and 8.3 assists, scored 17 points and dished out 12 assists in Monday night's 92-73 win over the Pacers. It was the Bulls' sixth straight win.
"He has a lot of toughness, both mental and physical," Thibodeau said of Rose on Tuesday. "He doesn't like to take any plays off. He doesn't like to take any days off. He attacks the basket, he gets knocked down, he gets back up. He'll keep going. He doesn't shy away."
Nick Friedell covers the Bulls for ESPNChicago.com and ESPN 1000. Information from The Associated Press was used in this report.