Flanagan played with Gerrard during the latter's distinguished career at Anfield, with the full-back enjoying a breakthrough campaign under Brendan Rodgers during 2013-2014.
Injury derailed Flanagan's progress, however, and he failed to make an impact during a season-long loan stint at Burnley.
A temporary switch to Bolton Wanderers came in January before Liverpool announced in June the 25-year-old would be released at the end of his contract.
That has given Gerrard a chance to swoop for a player he knows well - and Flanagan is determined to make the most of the opportunity to rekindle his career in Scotland.
"The size of the club and what the fans are about – I'm just delighted to be here and hopefully I can show the fans what I'm all about," he said.
"I played with the manager at Liverpool, and he was a big part of me coming here. I obviously know all about the club, but Stevie was a massive influence on me coming here as well."