Man United made the announcement in a post via the club's official website.
"Manchester United Academy defender Ben Hockenhull has completed a move to Championship club Brentford," the statement read in part.
"The young centre-back signed a third-year scholarship registration agreement with United after the Academy season was curtailed due to the COVID-19 global pandemic.
"Everybody at Manchester United would like to wish Ben well for the future following his departure."
Reacting, Brentford B head coach, Neil MacFarlane said: "First and foremost, Ben is coming from a top football club. He's somebody that has a fantastic presence on the pitch.
"As a centre-back, size is important in English football, but he has got much more to his game than that.
"He is fantastic on the ball and in possession, and with us being a possession-based team, that'll stand him in good stead. We think there is lots more development in Ben and he'll be a great addition to the squad."
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