The former 'Gers skipper opted not to transfer his contract over to the Glasgow clubs newco and has now signed a three-year deal with the Saints.
The 27-year old Northern Ireland midfielder returns to England's top flight after previous stints with Aston Villa and Fulham and he is thrilled to have been able to finalise his move despite interest from clubs in Germany and Turkey.
"I'm delighted to get everything done and dusted, and I'm looking forward to getting started," Davis told the club's official website.
"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."