The 29-year-old has signed a two-year deal with an option for a third season in a move that sees him link up with Carlo Ancelotti for the third time, having played under him at Bayern Munich and Real.
Ancelotti signed James from Monaco as Real manager in 2014, but the former World Cup Golden Boot winner failed to truly establish himself in the Spanish capital, before going on a two-season loan to Bayern in 2017, by which point Ancelotti was in control of the German side.
With one year left on his Real contract, James had been deemed surplus to requirements at the Bernabeu by Zinedine Zidane.
“I am really, really happy to be at this great club, a club with so much history, and here with a manager who knows me really well,” he said.
“I’m looking forward to achieving great things here – and winning things, which is what everyone’s aim is.
“I’ve come here to try to improve, to get better. I’ve also come here to help the team to win, to play good football – entertaining football.
“I’m convinced, with Carlo and his technical staff, we can achieve big things and one of the big reasons [I signed] was the presence of Carlo Ancelotti.
“I have enjoyed some great times with him previously at two different clubs. That was a massive reason to come here.”
James was appointed in the team of the tournament at last year’s Copa America, where Colombia got to the quarter-finals.
He has 76 international caps and 22 goals – in addition to 25 assists – following a debut versus Bolivia in October 2011, netting his first strike the following June in a meeting with Peru.
Rodriguez becomes the second South American midfielder to join Everton during this transfer window after Brazilian Allan arrived from Napoli on a three-year deal.
