The two sides had initially agreed a fee for the 27-year-old, who had previously accepted personal terms to transfer to the south-coast outfit after rejecting the opportunity to join the newly formed club, only to see Rangers block the Northern Irishman's request for international clearance, which was needed to complete the move.
However, an agreement has now been reached with a five-year deal penned, and the former captain praising his new club for their patience before joining the rest of the squad at their pre-season camp in Evian-les-Bains, France.
"I'm delighted to get everything sorted," Davis told the club’s official website.
"There was an element of uncertainty at how long it would take to get the transfer papers through, so I have to give credit to the Executive Chairman Nicola Cortese for wanting to get it done and removing the need for things to drag on any longer.
"This is good news for all parties, and now we can all move forward."
Southampton revealed how they worked hard to agree a deal, without Fifa involvement, which means the player will be available for the start of the season, unlike Davis's former team-mate Kyle Lafferty at Sion.
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"Both clubs have been in discussions to reach an amicable solution that would avoid the need for the player's international transfer clearance to be agreed at a Fifa tribunal," they explained.
"Saints' executive chairman, Nicola Cortese, has now reached a favourable agreement with Rangers that is in the best and fairest interests of all three parties.
"This negates any possible delay in the transfer proceedings and sees Davis's registration transferred to Southampton with immediate effect."
Sevco, the group that now own Rangers' assets, expressed their delight at the deal being wrapped up, hailing the Premier League club's part in negotiations and wishing the midfielder well.
"I am delighted that we have agreed terms over the transfer of Steven Davis," chief executive Charles Green added.
"Southampton have acted in good faith during the process.
"We wish them every success and they have signed a player who will undoubtedly make a great contribution to their club - just as he did at Ibrox."