The club, which has a history of running Prince's Trust programmes for disadvantaged young people in the area, has committed to fundraising for the charity throughout the season, in addition to the pro bono shirt contribution.
Last season, the club's three-year deal with Crown Paints, reported to be worth up to £5m, came to an end.
Set up by Prince Charles in 1976, the charity helps young people move into education, training and work.
Simon Williams, head of commercial and marketing at BRFC, said: "The club has enjoyed a strong and productive relationship with the Prince's Trust since 2005 and this agreement takes that relationship onto another level.
"The exposure the Prince's Trust will obtain as our shirt partner will greatly increase the level of awareness for the charity and, hopefully, encourage fundraising for the fantastic work they do to with young people."
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