The 20-year-old is no stranger to life under manager Craig Elliott, having already spent two loan spells with the Pilgrims in 2018-2019 and 2019-2020.
Gibbens has now linked up with United on a permanent basis ahead of their move to the Jakemans Community Stadium.
Elliott said: “I am delighted that Lewis has decided to sign for Boston United because obviously it’s a big decision for him to leave full-time football.
“I have watched him a lot over the past few seasons and I feel he will go from strength-to-strength by playing games and I have no doubt he has the right characteristics to one day go back into the EFL.
“He will give us great balance as a left-footed centre-back and I am really excited to sign a talented young player who wants to keep improving and be successful.”