The striker moves to the Seagulls, who are looking to bounce back to the National League South at the first time of asking following relegation.
“This signing is terrific business for the club, in Greg we have got a very good player who is in his prime, with experience and a winning mentality,” new Weston manager Scott Bartlett said on the club’s website.
“I was particularly impressed with Greg’s desire to play for the club which is important to me.
“He has had a hugely successful time at Chippenham under the guidance of Mark Collier and Gary Horgan who have done a great job.
“He has been a fantastic servant and I am sure he will be remembered fondly. This was a key position that we identified early on and in all honesty, it is probably a position we have not filled since the departure of Barks.
“Greg is a leader and is the competitive, dominant centre half we have been looking for and I’d like to formally welcome him to the club.”
Chippenham manager Collier confirmed: “Tins was offered a playing contract for the coming season and has declined a very good offer, of course I respect his decision and wish him well.”