The Club Captain signed a two-year extension this afternoon to keep him at the Club for a tenth season, and the 36-year-old says he didn't take much convincing to do so.
"I think the fact that I've been here for the amount of time that I have and then having the opportunity to stop on made this an easy decision," said Davis.
"I've got a lot of support at the Club so, with the way the Club is set up now and where it is going, I obviously wanted to be a part of that.
"To pretty much guarantee that the last of my playing days will be here is something that I've wanted to do for a long time.
"Since the Liebherr family has taken over with Nicola Cortese running the Club, it has been non-stop success so why wouldn't I want to be a part of that? It was an easy one for me."
Competition from Artur Boruc and Paulo Gazzaniga has meant Davis has made just nine appearances for Saints this season.
And the custodian admits he was left wondering whether his future lay away from St Mary's until he was given some reassurances by Executive Chairman Nicola Cortese and new First Team Manager Mauricio Pochettino.
"[The future] certainly popped into my head around Christmas, but a conversation between myself and Nicola made it a complete turnaround," he revealed.
"He reinstalled my belief that I was a part of the Club and that he wanted me to be a part of the Club in the long-term.
"I felt that I still had something to offer the Club as a player, and I wanted to show my support for the continued progression as we push on towards where we all want to see this Club go.
"The Chairman has made promises that he's kept, and probably done even more than he's promised.
"There's a lot of trust between the team and that man, so we're all very happy to be Saints players and we all want to be part of our continued success.
"The Manager came to me, so I don't think I'd have had any kind of extension if he didn't believe that I could still catch a ball!" added Kelvin.
"I wouldn't want to have a contract that was based on anything other than my ability. I'm very happy that discussions went well and that was obviously passed onto the Chairman.
"My job at this isn't always to be playing, but I want to feel that I'm still supporting the team, the Club, the Manager and the Chairman as best I can."
Davis has yet to make his first appearance under Pochettino, but he says he has been thoroughly impressed during the new man's first six weeks in charge.
As such, the goalkeeper says he is sure that Saints will secure their place in next season's Barclays Premier League despite their recent back-to-back defeats.
"The quality of what we've got in the dressing room means – and this is something that's sometimes hard to understand from the outside – that we don't feel that we are in a relegation fight," he insisted.
"Obviously the league table doesn't lie and we're not in the position we want to be, but we're convinced as a group of players that we should be further up than we are.
"The likes of myself, Jason Puncheon and Morgan Schneiderlin (who both extended their contracts last week) all believe that this club will be in the Premier League next season and we feel that it is moving towards where we all want to see it go.
"You've got to believe in this style of play and the philosophy the new Manager wants to promote, and you can see from our performances that the lads do," Davis added of Pochettino's start to life at Southampton.
"He's a very passionate guy. Without getting too deep, when you see someone with so much passion then it rubs off. Football is a passionate game and you need passionate people in it.
"I've certainly been impressed with him and his coaching staff – they are a tight group and you can feel that they want to improve every single player at this club, whether they are 16 or 36.
"I've certainly seen that first-hand because there's things they want to improve in myself.
"We've got to make sure that we don't focus too much on any negativity, but we're obviously not happy with the goals we're conceding at the moment," he continued. "We've watched them against and spoken about them, and we are working on them day-in day-out to improve in those situations.
"When a new manager comes in, he has new ideas and it does take a little bit of time. The ideal scenario is that you pick results up along the way, and we've done that to a certain extent – the Man City game was one that we possibly might not have won in the past.
"The Norwich game is an opportunity for us to pick up some points again and get ourselves back to where we feel we should be. We've missed a couple of opportunities in our last couple of games, so it's important we stay focused and tidy up on the things we've done wrong."