Beckham and Giggs were part of the infamous 'Class of '92' at United, playing regularly under legendary former manager Alex Ferguson as the club won numerous titles.
With Ferguson's replacement David Moyes sacked after less than a year in charge, Van Gaal and Giggs have been tasked with returning the club to the upper echelons of the top flight after finishing seventh this season.
While Beckham backed Giggs - who served as player-coach under Moyes before taking the reigns himself for four games following the Scot's departure in April - to impress as assistant to the experienced Dutchman, he revealed his surprise at the 40-year-old's decision to hang up his boots.
"I'm surprised he's retired because he was still playing great," he told Sky Sports News. "Physically he's still in great condition, to play for so many years at the top level you have to be in great condition.
"Now he has a new role at the club and it was great to see him walk out as Manchester United manager for those four games.
"When you've got someone like Giggsy, who all the players respect and all the fans love, it makes a huge difference.
"His role now has totally changed and I'm sure he will find it an easy transition because he takes things in his stride, he's not affected by anything.
"He knows the club better than most people who are at Manchester United now."
Van Gaal, currently in charge of the Dutch national side, will take over at Old Trafford following the FIFA World Cup in Brazil.
And Beckham, who won six Premier League titles at United before moving to Real Madrid in 2003, feels the former Ajax, Bayern Munich and Barcelona coach has the pedigree to turn United around.
"He has got a history of working with young players, bringing players through academy systems at places like Ajax," he continued.
"That can only be great for Manchester United.
"As a Manchester United fan and for Manchester United as a club, to have someone like this with his pedigree - he has worked with some of the biggest and best players in the world."
