The 22-year-old arrived in west London from Manchester United last January, and has made just six first team appearances under Ian Holloway.
The German-born midfielder, who can also operate at right-back having done so under Nicky Butt at United’s Carrington academy, passed a medical at the Glasgow club on Tuesday before making the move official.
Goss never made a senior appearance for Manchester United, however, was named in Premier League and Champions League squad.
“For me it’s a no-brainer really,” he told RangersTV. “Rangers is a massive football club with a massive fanbase as well, and being out there seeing the stadium was unbelievable.
“I know it is a tough league and there is a lot expected of the Rangers players. That is why I’m here – I want to challenge myself at a big club and I can’t wait to get going.
“[The experience of playing for Manchester United] will help. They are both massive clubs with a lot of fans all over the world. I am hoping to bring that experience with me.”