The 30-year-old is hoping for more first-team opportunities having been restricted to just three Carling Cup appearances for the Potters this term.
Griffin, who skippered Stoke to promotion from the Championship in 2008, has not figured in the Premier League for almost a year.
Stoke boss Tony Pulis: "There is a lot of competition for places in the squad and Andy is obviously desperate to play first-team football.
"A move to Reading is a great opportunity for him to go out and play regularly in the Championship."