The core of the legislation is exchanging 2,400 acres of land above the copper deposit, which is federally owned, for 5,300 acres of land owned by Resolution Copper that is used for recreational and conservation, as well as other culturally significant land throughout Arizona.
The companies have already invested more than $1bn on drilling and digging a 1.3-mile shaft on the land, which was opposed by environmental and native American groups.
Initially proposed nine years ago, the land swap was tucked away in the annual defence policy bill passed by the Senate and will now reach President Barack Obama to sign it into law.
Once the legislation is signed, Resolution Copper is set to focus on the comprehensive environmental and regulatory review under NEPA.
Following the deal, Rio Tinto and BHP Billiton will build a large copper mine in the state.
Resolution Copper Project director Andrew Taplin said: "Passage of the legislation means that Resolution Copper can move forward with the development of this world-class ore body, which will create approximately 3,700 jobs, generate over $60bn in economic impact and result almost $20bn in state and federal tax payments."
The companies said that operations at the Resolution Copper project are expected to start as early as 2020.
The Resolution copper mine is 55% owned by Rio Tinto and 45% owned by BHP.
Image: Resolution copper mine. Photo: courtesy of Resolution Copper Mining.