"I wish him all the best in the new project he is about to start in the United States," Calderon was quoted as telling television station Cuatro, by sports daily AS on Friday.
"He has been an example for this club and continues to demonstrate it day by day.
"I was a little annoyed when he said he was leaving because I wasn't expecting it, but he has made his decision and I am sure he will do well."
Beckham agreed a move to the Major League Soccer side at the beginning of the year, as his four-year contract with Real drew to a close. The five-year deal is worth over $250 million.
The 32-year-old midfielder is suspended for Saturday's Primera Liga clash against Espanyol at the Bernabeu.
He has four more league matches with Real left after that, as the club close on leaders Barcelona in the race for the Primera Liga title.