The 29-year-old said he was delighted to be staying on the south coast because Southampton were a progressive club, and that he was enthralled with the team's prospects.
"I'm excited to see where we can go together over the next few years," Davis said. "The club is run the right way and they try to do everything to their best ability.
"Nobody wants to stand still, we want to get better, that goes for the team and myself. I'd like to win trophies here and continually try to improve our league position. I feel we can do that at this club."
The Saints have confounded critics by storming to third place in the league after the first seven games, at the same time shrugging off an off-season exodus of big-name players including Adam Lallana, Luke Shaw and Dejan Lovren.
"It was a difficult summer for everyone involved, but the board stayed strong and the club made some really good signings in the manager and players that were brought in," Davis said.
"We've had an exciting start and we're determined to go on and keep progressing. Nobody wants to stand still."
Saints boss Ronald Koeman was earlier on Friday rewarded for his team's start by winning the Manager of the Month award for September.
Graziano Pelle, a striking replacement for another departee -- Rickie Lambert -- scooped the Player of the Month award, in another sign of the promise at St Mary's.
Koeman said: "I see Steven every day in training and in the dressing room. He is not a person who stands out by shouting a lot, but his professionalism and performances are what sets him apart and makes him such a good example for the rest of the players.
"Players like Steven are so great to have in your team, and also for the younger players who are looking to make it into the first team because they can see first hand what you have to do to become a player at the highest level like him."
Midfielder Davis, who started out at Aston Villa, joined Southampton from Scottish club Rangers in 2012.
(Editing by Alan Baldwin)
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