The right-back will link up with former Reds teammate Steven Gerrard, who took over as Gers manager this summer, at Ibrox.
"I'm delighted to be here," Flanagan told Rangers TV.
"When I spoke to Stevie, it was a no-brainer for me. The size of the club, what the fans are about, I'm just delighted to be here and hopefully I can show all the fans what I'm about.
"I played with him at Liverpool for many years and he was a big part of me coming here.
"I know all about the club, but Stevie was a massive influence on me coming here as well."