About 70 pieces of Caterpillar equipment will be delivered to Candelaria over the next three years.
Finning will also provide fleet maintenance services.
The company's South American president Marcello Marchese said the order was Finning's first significant one in Chile since the mining capital equipment market tanked in 2014.
"As activity in the mining sector begins to improve, we are well positioned to capture equipment and product support opportunities," Marchese said.
Finning International, headquartered in Vancouver, Canada, is the largest Cat equipment dealer in the world with locations in western Canada as well as Chile, Argentina, Bolivia, Ireland and the UK. Lundin's portfolio includes assets in Chile, Portugal, Sweden and the US.
Finning's share price has risen about 5.5% in the past week, capitalising the company at C$5.37 billion.