The defender joined the south coast club on a four-year deal on Wednesday after his contract with Crystal Palace expired.
However, due to his age, Saints may be required to pay compensation to the Championship outfit in a case that could go to a tribunal.
Clyne admitted that the aspirations of manager Nigel Adkins convinced him to move to St Mary's.
"I'm overwhelmed, really," the 21-year-old told Southampton's official website.
"As soon as I heard that Southampton were in for me, I was happy and I knew that this was the place where I could try to improve my football, further my career and get a chance to play in the Premier League.
"It's a club with a lot of ambition. The gaffer told me that they would want to be pushing for European football.
"We've got good players here - a young bunch of good, talented players who are destined for the top. So I don't see why we can't do it."
Adkins is now hoping that Clyne can develop into an established Premier League player with Southampton.
"We're delighted that we can finally announce that we've brought Nathaniel Clyne into the group to help us kick onto the next level," said Adkins.
"There's a lot of work going on behind the scenes all summer and, with [head of recruitment] Paul Mitchell and [executive chairman] Nicola Cortese, we work very hard behind the scenes to make things happen.
"For the last three years, Nathaniel has been a very attack-minded full-back who bombs on. He's got pace and he's a good one-on-one defender.
"He got into the Championship Team of the Year last year, and for such a young age he has had a lot of first-team football in the Championship.
"All being well, we can push him onto the next level now."
