Saints agreed to pay a fee to Gers to avoid any delays over his switch.
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," said Davis.
"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 Charles 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.
"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."