The former England captain has watched on as an interested spectator over the close-season as the Spanish giants - with whom he spent four years as a player from 2003 to 2007 - have looked to improve last season's UEFA Champions League-winning squad.
Rodriguez's arrival is the most high-profile at the Santiago Bernabeu ahead of the new campaign, with Real paying a reported €80million to bring in the playmaker from Monaco following a superb World Cup.
The Colombian arrives with his reputation at an all-time high, having won the golden boot in Brazil with six goals - including a stunning volley against Uruguay - as he helped his country to the quarter-finals.
And Beckham believes that by signing the 23-year-old his former club have secured one of the game's standout talents.
"He is a great player, obviously he had a great World Cup," said Beckham, who visited Real's training camp on Saturday as they take part in the International Champions Cup in the United States.
"He is a young player that is obviously very talented and who scored, for me, the best goal in the World Cup.
"As a Real Madrid and Manchester United fan, I am happy to see him at Real Madrid."