The 28-year-old was announced as Vincenzo Montella's first signing of the close-season on Monday after the two clubs agreed a deal for the Romania international.
Tatarusanu arrives in Serie A after a successful five-year period at Steaua that saw him claim two Romanian titles, including last season when the club finished five points clear of Astra Giurgiu.
After signing a contract in Florence, the goalkeeper said he was looking forward to testing himself outside of his home country for the first time.
"I can't wait to get stuck into this new professional experience," he told Fiorentina's official website.
"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."
Tatarusanu was part of the Romania squad that came close to qualifying for the FIFA World Cup, losing to Greece in the UEFA play-offs in November.
