The 24-year-old has one year remaining on his Wrexham contract and will move to Charlton in search of regular first-team football after falling down the pecking order.
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The Super Eagle joined the club initially on loan from Arsenal in 2023, helping the club secure back-to-back promotions before making his move permanent in 2024.
However, the arrival of Sunderland goalkeeper Anthony Patterson in a club-record deal, alongside Danny Ward, pushed him to third choice.
Okonkwo has made more than 100 appearances for Wrexham and played a key role in their rise to the Championship.
He switched his international allegiance from England to Nigeria and made his Super Eagles debut during the 2026 Unity Cup.