Pompey have confirmed the 31-year-old midfielder, who had two years left on his contract at Fratton Park, has completed his move to Elland Road.
"Chuck [Norris] had a fantastic season for us - he was a pivotal part of the team as a midfielder who gets goals," Appleton told Portsmouth's official website.
"He will be a real asset to Leeds. Neil Warnock will be delighted to have secured his services."
Norris, who joined Pompey on a free transfer from Ipswich in June 2011, is the fourth Pompey player to join Leeds this summer, following Jason Pearce, Jamie Ashdown and Luke Varney.