Burley had to fight off competition from Championship rivals Hull for Davies' signature, and was delighted to land the versatile England Under-21 international.
"He is a player I've admired for a while and he will give us extra options at the back," Burley told Southampton's website.
"He is a very promising player who has good ability and experience in the top flight. He is strong, quick and good in the air, he learned his trade with Middlesbrough and there were a few clubs after him.
"He's an ambitious lad and I'm pleased he's coming here."