Manager Ally McCoist has moved to add experienced competition to current number one Cammy Bell after the loan departures of Andrew Mitchell to Annan Athletic and Scott Gallacher to Airdrie.
Simonsen, who had been on trial at Rangers following a short spell with Dundee at the end of last season, could not contain his joy at joining the Ibrox side.
"I am delighted to join such a massive club as Rangers," he said.
"I have enjoyed my time training with the squad and everyone has made me feel very welcome in the short time I have been here and I am looking forward to the challenges ahead with this great club."
Rangers have sent two goalkeepers out on three-month loan deals this season. Mitchell has joined Annan Athletic and Gallacher has joined Airdrie.
Simonsen began his professional career with Tranmere Rovers in the mid-nineties before moving to Goodison Park where he spent six seasons with Everton.
With first-team opportunities scarce at Everton, Simonsen moved to Stoke in 2004 where he made 165 appearances in six seasons.
Simonsen lost his place in the side after the signing of Bosnian goalkeeper Asmir Begovic, forcing him to move to Sheffield United on-loan in search of first-team football.
After impressing on-loan, Simonsen made his move to Brammal Lane a permanent one and he made 108 appearances for the Yorkshire club before short spells with Preston and Dundee.