The KNVB have been looking for a new head coach since Dick Advocaat stepped down from the position in November after failing to reach the World Cup.
He will be expected to help the Dutch qualify for Euro 2020 and the World Cup in Qatar two years thereafter, reviving the team's fortunes in the process.
Guus Hiddink succeeded Van Gaal but was replaced by Danny Blind who was then followed by Advocaat in what has been a frustrating period for the Netherlands, who also failed to qualify for Euro 2016.
They also missed out on the European Championships in France in 2016.
Koeman made no secret of his desire to coach the Netherlands, and was disappointed not to have been appointed when Louis van Gaal left after the 2014 World Cup.
On Twitter, he wrote: "I am proud to finally announce that I am the new manager of the Dutch national team".
The 54-year-old former global defender is the seventh coach in eight years for the Dutch team, who have missed out on the last two major championships.
"We know we don't have the best players, but that doesn't mean that you cannot have the best team", he added.
Koeman said he will work players harder on the training pitch. The best way is so players can handle different systems.
"Koeman's sacking at Everton came as a gift from heaven for the KNVB", the popular De Telegraaf said.