The midfielder was said to have snubbed interest from Manchester City and Tottenham Hotspur in favour of Ibrox after meeting with Rangers boss Mark Warburton.
The 19-year-old is out of contract this summer and was free to move to Glasgow after negotiations on a new deal with Liverpool stalled.
A development fee would still have to be paid to his former club as Liverpool made an attempt to sign the player to a new deal. This will reportedly be in the region of £330,000.
Rossiter is a tenacious and tough centre midfielder with a decent touch and good eye for a pass. He has made five appearances for the first-team over the past two seasons, including one English Premier League fixture against Arsenal.
Warburton said: “Jordan is an outstanding young England youth international who will be an excellent addition to the Rangers squad.
“Technically gifted and game aware, he also has a first-class character and displays a tigerish desire to reach the highest levels of the game.
“It is a pleasure to welcome him to the club.”
Rossiter said: “I am made up to be here, it is a great club with a lot of history, you look at the likes of Rangers’ teams and players over the years and I am really looking forward to getting started.
“I have come from a massive club like Liverpool to another massive club like Rangers so it is a great feeling for me and an honour.”
“I know Frank McParland from my Liverpool days and working with the academy with him and he is a great fella. I am looking forward to working with him again and getting started here.”