The 23-year-old successfully passed a medical in Madrid this morning before agreeing a six-year deal and is scheduled to be unveiled in the Spanish capital this evening.
Rodriguez will join up with Cristiano Ronaldo, Gareth Bale and Karim Benzema to provide a formidable attacking threat for the Champions League winners.
Rodriguez was one of the stars of the World Cup, scoring six goals for his country on his way to winning the tournament’s Golden Boot award.
The attacking midfielder scored the goal of the tournament at the World Cup with a stunning volley against Uruguay in the last 16.
He makes the move to the Spanish capital after spending one season at Monaco, whom he joined from FC Porto for £35million last summer.
Rodriguez scored nine goals and registered 12 assists for Monaco last season as they finished second in Ligue 1 behind Paris Saint-Germain.
A Real statement read: "The player will be presented today, Tuesday 22 July, at 20:00 CET (7pm), in the Santiago Bernabéu's presidential box.
"Following that, James Rodríguez will take his first steps on the Santiago Bernabéu's pitch wearing the Real Madrid jersey and will then answer questions from the media outlets in attendance in the press room."
A statement on Monaco’s official website read: "The club would like to take the opportunity to thank James for the role he played in getting the club back to the Champions League and wishes him the very best for the future.
"The club had no intention to sell the player, however the time came when the solution of a transfer was considered to be the most beneficial solution for all parties.
"Monaco is proud to be a party to one of the most significant transfers in football history.
"Monaco is a club that will continue to grow and remains focused on the future. More than ever it has the ambition to strengthen the team and continue to progress for next season."
Rodriguez began his professional career with Colombian side Envigado before moving down to Argentinian club Banfield aged 17.
His performances for the Buenos Aires outfit attracted the attention of Porto, who signed him for £4million in 2010, and three years later he joined Monaco for £38.5million after helping the Portuguese side win a hat-trick of league titles and the 2011 Europa League.
@paulonbooks, I'm presuming they meant in terms of transfer fee. 63m is an awful lot of money which means Monaco who are already very wealthy, will now be able to spend quite a bit of money and be in accordance to FFP I'm assuming?- lfcfan80