One contract is for the processing facility, while the other is for the part-supply of a stacker, reclaimer and shiploader.
Rio said around 6200 tonnes of steel would be required for the projects, which would be sourced from Port Kembla and Whyalla, and fabricated at Civmec's Perth and Newcastle facilities.
The process facility includes a bauxite beneficiation plant and associated water, electrical and lighting systems to be constructed as modules and progressively transported to site for installation from mid-2017 until the end of 2018.
Rio said it was pleased to be working with Australian suppliers on the Amrun project.
"The Amrun project is a great example of the way Rio Tinto partners with local suppliers to deliver local jobs and economic benefits for the nation," Rio Growth & Innovation group executive Stephen McIntosh said.
"More than 550 Australian businesses have been engaged to date on Amrun, both directly and indirectly via contractors, and more than 50 Indigenous men and women are employed to work on the project."
The Amrun greenfields development, 40km south of the Weipa operations, comprises a bauxite mine, plant and port facilities on the Cape York Peninsula.
Proposed production is 22.8 million tonnes per annum, replacing output from the depleted East Weipa mine and increasing Cape York bauxite exports by around 10Mtpa.
The project has been designed with options to expand in the future to 50Mtpa.
The construction workforce is expected to peak at around 1100 ahead of first production and sales in the first half of 2019.