The 20-year-old defender, who has put pen to paper on a three-year contract, can play at either left-back or centre-half.
German-born Williams, 6ft 2in, made his only senior appearance for Villa as a substitute in a 1-1 Barclays Premier League draw with QPR in 2012.
Williams made eight appearances for the Republic of Ireland Under-19s and last year made his debut for the Under-21s against Italy.
He turned down the offer of a new deal at Villa to agree a switch to Ashton Gate, where he hopes to gain regular first-team football.
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