Jonathan Christie will continue in his role as managing director.
Mark Fenwick, chairman of Fenwick, said: "Williams & Griffin is a good strategic fit for Fenwick and will sit well with our current portfolio. We look forward to welcoming the staff of Williams & Griffin into the Fenwick Group."
Christie said: "I am delighted that Fenwick is to be our new owner. There is a great fit between our two businesses and this acquisition guarantees that the company will continue to go forward and invest in the store and the staff."
Williams & Griffin won the Drapers Department Store of the Year award in 2007. It has been owned by the Ireland family since the 1960's.
Fenwick was founded in 1882 and has 10 stores, two of which trade under the Bentalls fascia.