The Liga giants had been linked with a move for the creative midfielder ever since he impressed at the World Cup and the Colombian has now signed a contract until the summer of 2020 with the Santiago Bernabeu club after passing his medical.
James started his professional career with Envigado and also wore the Banfield and Porto jerseys before joining Monaco for €45m last year.
He impressed in his first season at the Ligue 1 side, scoring nine goals in 34 league appearances to help Monaco to second place in the table and qualification for the Champions League.
The attacking midfielder was also one of the stars of the 2014 World Cup as he picked up the Golden Boot and the Goal of the Tournament award following his sublime performances for Colombia, earning himself a move to Madrid in the process.
James is the Bernabeu side's second signing of the summer transfer window after the previous capture of Toni Kroos from Bayern Munich and will be presented to the world at 20:00CET on Tuesday.
The arrival of the Colombia star likely means the end of Isco's spell at Madrid, with Liverpool and Manchester City keeping a close eye on his situation in the Spanish capital.