Gooden, 18, features at full-back and joins the club from Charnock Richard.
He joined Accrington Stanley at the age of seven, playing in their youth ranks until the age of 14.
Gooden shared on social media: "I'm excited to be here at FC United of Manchester. Such a big club and looking forward to the challenge ahead."
Neil Reynolds has also added experienced full-back Andy White from Altrincham on a month's loan.
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