The plan is to combine the Terra end-to-end sensors, software and data delivery technology platform with Orica's Groundprobe geotechnical monitoring technology.
Groundprobe was Orica's first major acquisition to build its mining technology offering.
The Terra acquisition will be funded from existing cash and undrawn bank debt facilities.
The deal is expected to be completed in the first half of 2024, subject to regulatory approvals and other customary closing conditions.
Orica managing director and chief executive officer Sanjeev Gandhi said there had been an almost 10-year relationship between Terra and Orica.
"Terra is highly complementary to Orica Digital Solutions and our Groundprobe business, adding additional products and capability across the mining and civil infrastructure value chains," he said.
"The acquisition allows Orica to offer a more complete geotechnical offering to customers as well as adding an established stream of recurring software revenue.
"This acquisition strongly aligns with our Digital Solutions strategy and growth in mining infrastructure."
Terra CEO Mark Price said combining the two companies was a great next step in the evolution of Terra's end-to-end sensor and data delivery platform through working with Orica's Digital Solutions and Groundprobe businesses.
"This is a level of collaboration that is global-minded and future-focused," Price said.