The 21-year-old England Under-21 international has signed a four-year deal with the Premier League newcomers.
"I'm overwhelmed, really," Clyne told the club'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."
Clyne was out of contract at Selhurst Park, but he will still command a free because of his age. The two clubs are still in discussions over compensation and an independent tribunal will decide the fee if an agreement can not be reached.
Speaking after joining up with his new team-mates at their training camp in Evian-les-Bains, he added: "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."