The Northern Ireland midfielder, 23, completed the formalities of his switch from Fulham by signing a four-year contract with the Clydesdale Bank Premier League giants.
Davis, who starred at Ibrox in a loan spell during the second half of last season, was thrilled to be back on permanent basis following months of uncertainty over his future.
"I'm delighted. It's been ongoing all summer and great to get it finally done and dusted," he told Rangers World after joining for a fee believed to be in the region of £3million.
"It's been on and off all summer and I've been hearing bits and pieces throughout that time.
"You don't know what's going to happen and it took its toll."
Davis helped Rangers win two domestic cups and stage an incredible quadruple challenge towards the end of last term.
He added: "I thoroughly enjoyed my time here. It's a great club and I'm just glad to be a part of it again.
"I look forward to playing for the club for the next four years."
Davis is the fourth midfielder to join Rangers in just over a week and he believes the summer influx bodes well.
He said: "There's a good group of players and good players coming in to add to the quality that's already here. So hopefully a good season ahead."
Davis insisted he was not put off signing by Rangers' shock Champions League exit to FBK Kaunas and is determined to help them make amends by regaining the SPL title.
"I had an eye on the games and was disappointed when the lads went out," he said. "In the short-term, we'll have to concentrate on the league - that's the big one this year.
"We'll be fully focused on getting the title back. After that, if we get back into Europe then we'll concentrate on that."