Adams, who scored 22 goals last season, has signed a five-year deal after undergoing a medical on Sunday and agreeing personal terms.
“I'm delighted that it has all gone through. There was interest in January but it didn't quite go through but I'm happy now it has," he said.
"You can see with the track history – the amount of young players they're playing, the gaffer's belief in the young players, the squad in itself – where the club is going to be. I want to be part of that.
“That's something I noticed straight away. Even watching from the side when I was at Birmingham and I was watching Southampton play, I liked what Ralph did so when the opportunity came up I couldn't say no."
Adams is looking forward to joining up with his teammates and making his mark on the Premier League.
He added: “It was a massive season for me last year and obviously Southampton have picked up on that and added me into the squad. I'm delighted with that and I can't wait to get going.
“It's a new step and there's different players who I haven't played with but I can't wait for the challenge.
“It's about proving myself again and proving to my teammates that I can play with them and we can make something happen."