Williams, who served the Ewood Park club for 13 years but departed shortly after the Venky's group completed their takeover, will join City on July 1.
City chief executive Garry Cook told the club website: "John Williams is a hugely respected figure in the football world and I admire him greatly. Unsurprisingly, a number of organisations were keen to work with him and I was therefore delighted when he accepted my offer to join us.
Cook added: "We must ensure that our targets are not impacted by the high volume of daily operational tasks. John's support of Brian (Marwood, Football Administration Officer) and the football operations team will enable us to ensure those targets are met and he will be a great asset to the club."