Clements replaces Joe Philbin, who left last month to become the Miami Dolphins' head coach, the Milwaukee Journal Sentinel reported.
"Tom has been an integral part of our success and our staff, making it an obvious decision to promote him to offensive coordinator," McCarthy said in a statement released by the Packers. "He has earned this opportunity and we look forward to continued offensive success in 2012."
Clements had run the Buffalo Bills' offense for two seasons before joining the Packers in 2006.
Neither McCarthy nor Clements was available for comment on the move.
Clements, 58, had interviewed for head coaching jobs for the Tampa Bay Buccaneers and Penn State University, but both teams chose another candidate.
"I'm happy that [the promotion] happened and I'm happy for Joe [Philbin] that he's a head coach, and I'm glad I was able to step into his place," Clements said in the release. "I've been a coordinator before, only for a few years. I've always wanted to get back to doing that and I'm thankful that it's here in Green Bay."