In an unusual move, the Dutch football association, the KNVB, confirmed Hiddink's contract would run only to the end of Euro 2016, after which time assistant coach Danny Blind will assume control and lead the bid for qualification to the 2018 World Cup.
Former Holland and Manchester United striker Ruud van Nistelrooy also joins the coaching set-up as an assistant to 67-year-old Hiddink, working alongside Blind.
The outgoing Van Gaal, who comfortably led Holland to World Cup qualification, confirmed last year that he would not look to extend his deal beyond this summer's tournament in Brazil, and has been linked with the likes of Manchester United and Tottenham.
Friday's announcement confirms Hiddink's second spell in charge of the Oranje, having previously led his country for three and a half years from 1995, culminating in a fourth-placed finish at the 1998 World Cup in France.
In a statement, the KNVB confirmed: "Guus Hiddink, Danny Blind and Ruud van Nistelrooy form the new technical staff of the Dutch team.
"They go to work after the 2014 World Cup in Brazil. The KNVB has a contract agreed with Hiddink that connects him from 1 August 2014 to the European Championship in 2016 in France as coach. Blind and Van Nistelrooy are appointed for the same period as an assistant coach.
"After Euro 2016, Blind will replace Hiddink as coach, extending his contract with the KNVB to the 2018 World Cup in Russia."
Hiddink, whose wide-ranging career at international level has also taken in spells in charge of South Korea, Australia, Russia and Turkey, was delighted to be handed the reigns for a second time.
"I am honoured to return as coach for the Dutch team," he said. "With Danny Blind and Ruud van Nistelrooy we also have a solid team with a lot of football knowledge and experience.
"It is wonderful that I can oversee my own succession. In this way the football vision for the Dutch team in the long term can be guaranteed."
KNVB director Bert van Oostveen added: "With Hiddink we get a coach with a wealth of international experience and successes. He has proven his ability as a trainer.
"We are also very pleased with the further development of the technical staff. Blind recently proved his worth at the KNVB. In the next two years he has a chance to grow.
"With Van Nistelrooy, we again add a former international football player to the staff. It goes without saying that we have a lot of faith in this coaching staff."
Blind has been an assistant coach in the national set-up since 2012 and was seen as a key component is the management team that presided over nine wins and a draw from 10 World Cup qualifiers.
The former Ajax and Holland defender has previous top-flight managerial experience, having served as head coach of Ajax between 2005 and 2006.
Holland have been drawn in Group B for the World Cup beginning in June, alongside reigning champions Spain, Australia and Chile.