Akinmboni, 18, moves to Dean Court for a mooted €1m.
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Bournemouth technical director Simon Francis said: "He is an exciting young player we have been monitoring for an extended period and have been impressed by his progress.
"Matai is a player we believe has a very bright future and we are looking forward to seeing him develop with us."
Akinmboni made his debut for DC United at 15 years of age in 2022.