The five-year contract is for stockpile rehandle services.
Thiess has been working at Prominent Hill since 2006, providing open pit services.
CIMIC executive mining and mineral processing and Thiess managing director Douglas Thompson said the company had a strong working relationship with OZ.
"Since we first began work with the team 12 years ago, we've focused on understanding OZ Minerals' priorities, and have continually challenged ourselves to provide flexible services, delivering operational excellence and long-term value to our client."
Thiess will begin work next month.
CIMIC shares last traded at $42.40, valuing the company at $13.75 billion.