The two clubs have agreed an undisclosed fee for the Northern Irishman, reported to be around ?800,000.
The midfielder, who has signed a contract until 2016, originally agreed to join Saints earlier this month but a question mark hung over the deal, with Ibrox chief executive Charles Green challenging the legal right of several Rangers players not to transfer their contracts to his newco club.
Davis, Steven Naismith, Jamie Ness, Kyle Lafferty and Steven Whittaker were faced with the prospect of delays to their transfers pending clearance by FIFA.
The world governing body on Friday gave provisional clearance to Ness to commence his career at Stoke, while the Scottish Football Association confirmed clearance had also been granted to Lafferty, Whittaker and Naismith for their respective moves.
However, Southampton were happy to forgo any intervention from FIFA and negotiated a deal directly with the Scottish club.
A statement on saintsfc.co.uk said: "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' registration transferred to Southampton with immediate effect."
Davis, who has been training with Southampton since agreeing to the move on July 6, welcomed the news that the deal was now concluded. "I'm delighted to get everything sorted," he said.
"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."
Rangers chief executive Green also expressed his satisfaction that a deal had been reached, telling Rangers' official website: "I am delighted that we have agreed terms over the transfer of Steven Davis. Southampton have acted in good faith during the process."