The former Chelsea interim manager takes over from Van Gaal who led the Dutch to third place at this year's World Cup.
"There will not be many changes," said Hiddink at a press conference to mark his second spell in charge of the national side having led them to the last four of the World Cup in 1998.
He has already hinted that Manchester United striker Robin van Persie is likely to remain as captain while Arjen Robben of Bayern Munich will continue in his role as vice-captain.
Hiddink's contract runs through to the end of the 2016 European Championship in France, after which he will be replaced by current assistant Danny Blind. His other assistant will be former Manchester United Dutch striker Ruud van Nistelrooy.
"I felt great enthusiasm on starting my first official day of work today," Hiddink said. "First and foremost, bravo to the team, both the players and the technical staff who worked under Louis van Gaal.”
United boss Van Gaal had been widely criticised by the Dutch press prior to the World Cup, accusing him of turning his back on the traditional Dutch style of attacking football.
But his new counter-attacking system, with three central defenders, proved successful, taking the Netherlands further than expected and producing a stunning 5-1 victory against the holders Spain.
Hiddink indicated he wished to keep faith in the 'Dutch school' while also hoping to maintain the "instinct of survival" instilled in the team by van Gaal.
The 67-year-old also took South Korea to fourth place at the 2002 World Cup before spells in charge of Russia, Turkey and Australia and a brief period at Stamford Bridge, where he led Chelsea to the Champions League semi-finals in 2009.
He had been out of coaching work since leaving Russian side Anzhi Makhachkala in July of last year.