The 17-year-old made an impressive start to the season after being promoted to the first team squad last summer, making his first start in the second round of the Capital One Cup at Stevenage in August and his Premier League debut in November against Swansea City.
Shaw's introduction to the team coincided with Southampton moving away from the foot of the league table, as they put together an impressive string of results that has seen them beaten just twice in their last ten league games.
The left-back, who has attracted attention from a number of Premier League sides including Arsenal, cannot sign a senior contract until his 18th birthday in July, and it is understood he will be signing a five-year deal.
"I have spoken with the chairman about a long-term plan for me at the club," Shaw told the club's official website.
"To put an end to all the speculation, I will be committing my future to Southampton. I'm not going anywhere.
"I think Southampton is the place to be for young kids like me. I'm playing in the Premier League for the first team and that is all anyone wants to be doing, so I just want to carry on."
Shaw followed in the footsteps of fellow youngster James-Ward Prowse, who signed a five-year deal last November, and he praised the club's youth system.
"I have been at Southampton since a very young age so I've been here a long time now. I think they are happy with me here, and this club is great for young players like us," he said.
"If you look back over the years, Adam [Lallana] has come through the youth system and now he is the captain of the first team, and Prowsey (James Ward-Prowse) has just signed a five-year deal - and that is what I want to be doing.
"We have a lot of trust in our youth and there are more players coming through next year, so hopefully we will just carry on going."
Looking ahead to the weekend's trip to Aston Villa, Shaw added:"This will probably be our biggest game of the season.
"We know that we can beat them so, if we go there and play our game, I'm sure we can get three points.
"We have a few games coming up that we can go and get points from and I believe we can do that.
"I think we will stay in the Premier League. We have been playing some superb football but the luck hasn't gone our way recently."