Defender Goldson has joined the Scottish side for an undisclosed fee having struggled for action last season.
The 25-year-old had preventative heart surgery in February last year and was unable to force his way into the Albion starting side on a regular basis, with Lewis Dunk and Shane Duffy ahead of him in the pecking order.
Brighton weren’t actively looking to sell the former Shrewsbury man but Hughton indicated he felt he couldn’t stand in Goldson’s way as he will have the chance of regular football at Ibrox.
‘Connor has done extremely well for the club in the three years he has been here, but he wants to play regular senior football, and at this stage we cannot give him that guarantee,’ Hughton told the club’s official website.
‘Lewis Dunk and Shane Duffy were exceptional last season, and very consistent in the central defensive positions, which left Connor with very limited opportunities, and I totally understand his position and desire to want to play regular football.
‘He has been a great professional and a pleasure to work with – and he has shown a great mental strength to come through a very tough time after he underwent crucial heart surgery just over a year ago.
‘On behalf of everyone at the Albion, I would like to thank Connor for his time at the club and wish him all the very best for the future at Glasgow Rangers.’