The 23-year-old will finalize personal terms Monday before being officially announced as the Champions League winner's second signing of the summer transfer window.
In an overall deal that should see the Colombia international become the third most expensive player in the history of the game, Madrid will meet the French club's 88 million-euro valuation — the same fee Barcelona paid for Luis Suarez — including performance-related variables.
With an agreement reached between the two clubs over the weekend, discussions have been scheduled for Monday to iron out the details of Rodgriguez' personal terms as Madrid aims to make the midfielder its second signing of the summer following the arrival of Toni Kroos from Bayern Munich.
An understanding of the 23-year-old's salary has been in place since Madrid president Florentino Perez decided to target the player as this summer's principle Galactico signing.
The arrival of the 23-year-old could spell the end for Isco at the Santiago Bernabeu, with Liverpool among the clubs monitoring the playmaker's situation.
In addition to the acquisition of World Cup Golden Boot winner Rodriguez, Madrid has been working on a deal to bring a second Colombia star, Radamel Falcao, from Monaco and reached a breakthrough in talks at the beginning of July.
Falcao's return to Spanish soccer after a season in Ligue 1 is dependent on Madrid's medical department declaring itself satisfied with the striker's recovery from cruciate ligament surgery.