The 22-year leaves Town after joining the club eight years ago and moves to the Amex for an undisclosed fee.
Goldson was the longest-serving player at the Greenhous Meadow, and made 120 appearances in total for the Shrews, scoring eight goals.
During his time at Shrewsbury, the centre-back won two promotions from League Two to League One – last season and in the 2011/12 campaign.
Hughton told the club’s official website: “We are delighted to bring someone with Connor’s ability and potential to the club; at his age there is still plenty to come from him. We know he had a lot of admirers in terms of other clubs, so we are thrilled to complete the deal.
“He is predominantly a central defender, but he has also played in midfield and at right-back, and it is clear by his goal record last year that he can also contribute in that area too.”
Shrewsbury chief executive Matt Williams added on his club’s official website: “I think the deal we’ve got is in the best interests of Shrewsbury Town and it helps the player to establish himself further up the ladder before we get there.
“From the club’s point of view you always want the best possible deal for the club and I believe we have got that.
“We were not aware of Brighton’s interest before the start of the week, and it was Connor (who) declared himself unfit for selection on Monday evening.”