During his playing career, Koeman made 78 appearances for the Dutch national side.
The Dutch football federation - the KNVB - announced on its website that Koeman has signed a contract that runs through to the 2022 World Cup in Qatar.
Koeman, sacked by Everton in October, replaces Dick Advocaat, who stepped down previous year.
The Netherlands also missed out on UEFA EURO 2016 prior to Russian Federation 2018, so Koeman's task will also be to get the Dutch back to the continental finals, which will be held in 12 cities in 12 different host countries.
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"I am really excited and really proud", Koeman said at his introductory press conference. We did not qualify for this World Cup or the last European Championships but we still have a lot of good players. I'm really positive about the future of the national team.
Koeman, who earned 78 caps for the Netherlands, succeeds Dick Advocaat, who had been brought in midway through previous year after the sacking of Danny Blind in March.
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.
The Dutchman has also worked at Vitesse, Ajax, Benfica, PSV, Valencia, AZ and Feyenoord and was previously assistant at Barcelona and the Netherlands.