They were runners-up at the 2010 World Cup and finished third in Brazil four years later but failed to qualify for the 2018 finals in Russian Federation.
His contract will see him in charge up to and including the 2022 World Cup in Qatar.
Koeman, 54, replaces Dick Advocaat, who was appointed as a stop-gap measure in June after Danny Blind was sacked.
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They also missed out on the European Championships in France in 2016.
Since finishing third at the 2014 World Cup under Louis van Gaal, the Netherlands have endured a rocky few years.
On Twitter, he wrote: "I am proud to finally announce that I am the new manager of the Dutch national team". "I think the best is that players can handle different systems because we know we don't have the best players but that don't mean you cannot have the best team". "We don't have the best players, but that does not mean you can not have the best team".
But instead, the Royal Dutch Football Federation (KNVB) appointed another stalwart Guus Hiddink, who was then replaced by Danny Blind, followed by Advocaat - all in just over three-and-a-half years.
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Koeman said he will work players harder on the training pitch.
Koeman played 78 internationals for the Netherlands at a time when the Dutch team was famous for sticking to an attacking 4-3-3 system.
"Koeman's sacking at Everton came as a gift from heaven for the KNVB", the popular De Telegraaf said.
After finishing seventh in his first season at Everton, Koeman was sacked with the Toffees 18th in the Premier League table despite spending around £150million on new signings in the summer.
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