Connelly replaces Tim Drevno, who left USC after one season to become offensive coordinator at Michigan under Jim Harbaugh.
"He is a great fit for what we do," Sarkisian said in a statement. "He is very familiar with Pac-12 and West Coast football, and he is also very versatile as he has coached various offensive styles in his career."
Connelly inherits a young but experienced offensive line.
The entire starting line and several backups who played extensively last season return, including rising senior center Max Tuerk, sophomore guards Viane Talamaivao, Damien Mama, junior Zach Banner and sophomore Toa Lobendahn, who started at guard and tackle.
Junior tackle Chad Wheeler, who started at left tackle, is expected to return after midseason knee surgery.