The England youth international will link up with the Scottish club at the end of the season after agreeing terms on a deal that will run until the summer of 2020.
The 19-year-old has made four first-team appearances for Liverpool this season and made his Premier League debut against Arsenal in August 2015.
A hamstring problem harmed his involvement in the second half of the campaign, however, and Rangers have boosted their squad for the new Scottish Premiership season with the signing of the teenager.
"Jordan is an outstanding young England youth international who will be an excellent addition to the Rangers squad," boss Mark Warburton told the club's official website. "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."