Moniz ruled himself out of the running to take over at Meadow Lane last week due to family reasons but has now agreed to take the helm.
The Dutchman has six games to save County from League One relegation, with the club sitting a point adrift of safety.
County have been without a permanent manager since parting company with Shaun Derry on March 23. Paul Hart and Mick Halsall have taken charge of the team in the interim.
Moniz, who has previously been on the coaching staff at Tottenham, led Austrian side Red Bull Salzburg to a league and cup double in 2012.
His first game in charge comes against bottom club Yeovil Town on Saturday.
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