The 28-year-old goalkeeper, who spent the past six seasons with Steaua Bucharest and had a season on loan at Gloria Bistrita in 2008, left the Romanian side at the end of the season on a Bosman ruling after rejecting a new contract offer.
During his time at Steaua, Tatarusanu helped them win two Romanian championships, one Romanian Cup and two Romanian Super Cups before signing for the Serie A club on Monday after passing a medical.
Tatarusanu, capped 24 times by his county, told violachannel.tv: "I can't wait to get stuck into this new professional experience.
"I've wanted to come to Fiorentina from the start because this club has ambitious plans.
"The team plays entertaining football, the fans are passionate and they're at one with the team and the city. Plus Florence is one of the most beautiful cities around, it's the birthplace of Italian art."