The 25-year-old has signed a pre-contract with Peterborough and will join the club on a free transfer when his Wrexham deal expires in the summer.
Posh director of football Barry Fry told the Peterborough Evening Telegraph: “We have signed Nathaniel on a pre-contract and he will join us at the end of the current season.
“The manager went to watch Wrexham and Brighton in an FA Cup tie and liked what he saw of Nathaniel.”