The consideration comprises $6.5 million cash up-front and up to $100 million in the form of a contingent payment linked to uranium spot prices and the mine's net income for the next seven calendar years.
Rio will also receive a cash payment if CNUC sells the Zelda 20 uranium deposit.
The sale follows a strategic process run by Rio to assess its options.
"The sale of our interest in Rössing once again demonstrates our commitment to strengthening our portfolio and focussing on our core assets, which deliver sector leading returns in the short, medium and long-term," Rio CEO J-S Jacques said.
Rössing produced 4.65 million pounds of uranium oxide last year, of which Rio's share was 3.19Mlb.
Rio recorded a $267 million impairment on Rössing last year due to "oversupply in the uranium market resulting in structural changes to forecast pricing".
Rio also holds 68.4% of Northern Territory uranium producer Energy Resources of Australia, and 100% of the Roughrider uranium project in Canada.
The other shareholders in Rössing are the Iranian Foreign Investment Company (15%), the Industrial Development Corporation of South Africa (10%), Namibian government (3%) and individual shareholders (3%).
The transaction is expected to close in the first half of 2019.
Shares in Rio were down 3.5% in afternoon trade to A$74.12.