Fredrick joins Simoiben FC on a four-year deal with the club having the option of an extra year.
The Nigerian defender has spent the season on-loan with the B team and made the bench for Premier League and FA Cup games.
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Fredrick told the club's website: Signing permanently for Brentford is a great moment for me and my family and I want to thank everyone who started this journey with me.
Neil and the rest of the coaching team have been very patient and supportive throughout this season and they have helped me become a stronger more confident player in the process.
"I want to repay the club's trust in me by continuing to do my best and pushing to even greater heights."