The programme is created and executive produced by Kurt Sutter, the man behind Five's police drama The Shield. It follows a notorious motorcycle club that doubles as an illegal arms business.
The show stars Queer as Folk actor Charlie Hunnam, who plays Jackson Teller, the series' principle character, and award-winning actor Ron Perlman, star of Hollywood's Hellboy franchise.
The 13 x 60-minute series originally aired in the US on FX last year and became the cable channel's most successful new series among adults since firefighter drama Rescue Me in 2004.
It also managed to outperform Sutter's other FX US drama, The Shield, and was recently green-lit for a second 13 x 60-minute season.
The deal was closed by Bravo channel controller Dave Clarke and 20th Century Fox Television Distribution's senior vice-president and managing director of sales Steve Cornish.
“US cable drama is the best in the world and FX is a past-master,” said Clarke. “We are proud to have secured such a high-quality and successful series for our viewers.
“This acquisition is part of Bravo's commitment to increase our primetime quality programming. Sons of Anarchy will be essential viewing for UK fans of both high-quality action and premium drama.”