The 27-year-old was captain of the beleaguered Scottish side but left after rejecting a transfer to the newco club.
Davis follows the likes of Kyle Lafferty and Steven Whittaker out of the club and has joined newly-promoted Saints until 2015.
Davis told the official Sotuhampton website: "I'm delighted to get everything done and dusted, and I'm looking forward to getting started.
"There was quite a bit of interest in me from other clubs but, after speaking to the chairman and the manager, I saw the level of ambition the club has shown.
"They've had a lot of success over the past couple of years to get to this stage, and they don't want to stand still - they want to keep moving forward, and that was a big thing for me.
"Now I'm just looking forward to getting down, getting to know the boys and getting started."