The Scottish Premier League giants confirmed Commons had wrapped up his transfer from the Rams after passing a medical and agreeing medical terms on Thursday. The 27-year-old has signed a three-and-a-half-year deal after Celtic paid a transfer fee believed to be around £300,000.
Celtic manager Neil Lennon played with Commons when the duo were at Nottingham Forest, and had been desperate to sign his former team-mate in the face of competition from Old Firm rivals Rangers.
Derby chief executive Tom Glick meanwhile expressed disappointment that Commons had chosen to quit Pride Park.
"It is disappointing to lose Kris, he is a very talented footballer and we always wanted him to stay," Glick said. "We did everything we could to make him stay and we offered a very good deal to him."