The 27-year-old left West Ham United to sign for the Saints on loan for the entire season.
Cornet has revealed that he spoke to manager Russell Martin and former teammate Flynn Downes about moving to St. Mary’s Stadium.
"It was a long deadline day but it's finally done and I am happy to be here. I am excited to start working with the club," Cornet said.
"I heard of the interest from Southampton for the first time five days before the end of the transfer window, and I had a chat with the manager.
"The way that he spoke to me was really good and he convinced me to change my club and I am really happy."
The Ivory Coast international added: "I know Flynn from playing together at West Ham, and I know Charlie Taylor from Burnley and we had a good time.
"I asked Flynn about the club and the training ground before I joined. He told me everything is amazing so I said, 'Okay, let's go."