The 24-year-old full-back has signed a two-year deal, having turned down the offer of a new deal with the Pilgrims.
"The last couple of years at Boston I've always wanted to make the step up," said Mills.
"I'll be jumping two steps, but I'm sure I will pick it up quite quickly."
Mills' arrival follows the signing of fellow full-back Danny Andrew from League One side Fleetwood Town.
Promoted Grimsby Town have made their second signing since returning to the Football League by bringing in defender Zak Mills from National League North neighbours Boston United.