Gunn, 22, spent seven years at Manchester City before signing a five-year contract at Hughes' Southampton.
The goalkeeper was praised by English media throughout his loan last season at Championship side Norwich City, and decided to join 'Saints' because of the plans the club has for his future.
Speaking to 'Sky Sports', Gunn said: "There were different options I had - possible loans, possible permanent moves -and I was weighing everything up.
"Then I met Dave Watson and the manager, and that was the biggest thing that sort of swayed it really - the way they spoke to me and wanted me here was probably the biggest thing that I took from the summer and that's why I'm here.
"Obviously I'm a younger player, so they are looking more into the future and looking to make me a better player all-round."