Barmby, 34, is fulfilling a lifelong ambition by playing for Hull in the top flight and his son's decision has come as a surprise to the Hull board.
However, they cannot prevent Barmby Jnr leaving. United have been tracking Barmby's son for two years but they did not expect to sign him before he was 16.
Hull are not entitled to any compensation for the player because he was too young to sign for them.
Barmby, who is a left midfielder like his father, made his debut for United's academy side last Saturday.