Peterson asked for and was granted his release from the Razorbacks earlier this month. He's eligible to play immediately for the Seminoles because he graduated from Arkansas in May.
Peterson spent two seasons at Arkansas, sitting out the first year after transferring from Iowa. He started 23 games last season and averaged 6.3 points per game.
He played two seasons at Iowa before that, averaging 10.6 points and 4.2 assists per game as a sophomore.
Florida State coach Leonard Hamilton said in a statement that Peterson's maturity and experience would help the Seminoles on and off the court.