The Pioneer Press had reported Saturday that a deal was close to being finalized.
The new contract includes $41 million guaranteed and pays more than $42 million over the first three years, according to ESPN.
The NFL's current highest-paid cornerback is Norman, who signed a five-year deal last year worth up to $75 million.
Rhodes is under contract in 2017 for $8.026 million, meaning he has six years and $78 million on a contract that runs through 2022.
This move comes days after the Vikings extended the contract of defensive end Everson Griffen. The 2013 first-round pick finished with 44 tackles, a career-high five interceptions and one forced fumble.
The Minnesota Vikings have agreed to a lucrative contract extension with their premier cornerback.
It's the second time in as many weeks that the Vikings have locked up a defensive starter.
The Vikings also have an interest in an extension for linebacker Eric Kendricks when he is eligible for one after this season.