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.
"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."
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