The 23-year-old scored the goal of the tournament and bagged the Golden Boot as Colombia reached the last eight in Brazil and was snapped up for around €80 million (£63m) by Los Blancos.
Beckham, who turned out at the Santiago Bernabeu between 2003 and 2007, can foresee James becoming a Madrid great and praised him for his performances in the World Cup.
"The club's brought in some very special players and that has strengthened the team," the former England captain told reporters at a visit to the club's United States training camp.
"This club will always have players who are different and James is a great player - he had a great World Cup and scored the goal of the tournament."
Beckham played during the club's 'Galacticos' era but failed to win the Champions League during his four years in the Spanish capital and hailed the way in which Carlo Ancelotti - with whom he worked at Paris Saint-Germain and AC Milan - took Madrid to 'La Decima'.
"I know how important the Champions League is to Real Madrid and I'm happy for Ancelotti, the president, the lads and the fans," the Englishman added.
"It was incredible, it was such a special season. I won the league with Madrid and that was amazing - I can't even begin to imagine what it must have felt like to have won the Champions League with Madrid.
"I'm always happy to see Real Madrid. I really miss being at the club."