Los Blancos agreed to pay Monaco a staggering €80 million (£63.2m) for the Colombia international - despite doubts over whether there is room within Carlo Ancelotti's star-studded starting line-up for an attacking midfielder.
However, Pepe has been watching James's development with interest ever since the No.10 joined his former club, Porto, and is in no doubt that the 23-year-old will prove a fantastic addition.
"He's a very talented player," the Portugal defender enthused to Marca. "I saw him when he played at Porto and he has a very good left foot.
"It's amazing that Madrid have signed such a great player."
Meanwhile, Pepe is confident that Cristiano Ronaldo will be fully fit for the start of the new season, even though his international and club team-mate has been troubled by thigh problems in recent months.
"Cristiano had time to relax and unwind with his family," the centre-back remarked. "He's well and I think he'll be at his best."