Davis, who enjoyed an outstanding two years at the Hawthorns will play for former Brigg boss Steve Housham's side who currently play two levels above the Zebras.
Brigg boss Mick Gray said, "Whilst I'm obviously disappointed to lose a player of Liam's calibre, I can fully appreciate that he wants to play as high as he can. We have all enjoyed working with him and wish him every success at Gainsborough, with his ability and first class attitude he certainly deserves to do well."
Brigg Town would like to thank Liam for his efforts and will follow his progress with interest