The former Everton boss was in to replace Louis van Gaal, who left after the World Cup in Qatar.
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Such an appointment was made in April last year, but it was revealed Koeman would take up the position at the start of 2023.
His contract with the Dutch national team will run until the next World Cup, which takes places in 2026.
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Koeman was last in charge of the side from 2018 to 2020 before he became the manager at Barcelona.
He was on hand to help them qualify for Euro 2020, where they were knocked out by the Czech Republic in the Round of 16.
Upon his return to the role, Koeman revealed he will look to play aback four as opposed to a back three used under Van Gaal.
In a press conference on Monday, he said: "In principle, we are going back to the system we played before.
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"I will sometimes change systems, but we will follow the basic principle of four defenders."
A Euro 2024 qualifier against France in March will be his first match back in action as the Netherlands manager.
He had limited success in his previous role at Barcelona and was also unable to get the best out of Everton before he left in 2017.
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The Toffees have had five permanent managers since his departure, with Frank Lampard being the latest name to lose his job at Goodison Park.
Marcelo Bielsa is an early contender for the role, with Sean Dyche also emerging as a favourite for the now vacant job.