The former Everton and Southampton boss takes charge of a team who have failed to qualify for this year's World Cup.
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's first press conference was immediately announced by the KNVB, and he was set to speak about his new role at 3.30pm GMT.
He succeeds Dick Advocaat, who stepped down after the team's failure to reach this summer's finals in Russia.