APOEL confirmed the transfer in an official statement, describing the Czech Republic international as a player who "has left an important mark on European football pitches."
The Cypriot club, who signed Barák on a two-year deal, outlined his path through the game: starting his professional career at home before moving into Serie A with Udinese, Lecce, Hellas Verona and Fiorentina, reaching a UEFA Europa Conference League final along the way and earning 44 caps for his country.
"Antonín Barák enters the APOEL family bringing quality, experience and an important wealth of experience at the highest levels of European football," the statement read.
"We welcome Antonín into the APOEL family."
The move brings to a close a nine-year, two-month association with Italian football and a four-year spell specifically with Fiorentina, the last two seasons of which were spent out on loan at Kasımpaşa and Sampdoria.
Barák leaves having made 90 appearances and scored 11 goals for the Viola, his standout moment arriving with a decisive extra-time winner against Basel in the Conference League semi-final — a goal that earned him a lasting nickname among supporters.
The 30-year-old marked his exit with a lengthy message posted to social media.
"After 9 years and 2 months, the time has come to change scenery and, after 4 years, to change club," Barák wrote. "A beautiful chapter closes at the club that gave me so much, and I couldn't ask for more. I want to talk about so many things: the pride of wearing this beautiful shirt, representing a wonderful city, meeting fantastic people, becoming part of the Viola people and becoming one of you! So many things and memories will stay with me that I can't describe with words alone.
"It was a beautiful journey, and every time I start thinking back on it, it almost makes me cry with happiness that all of this was possible. Many of you call me 'the man of Basel.' You can't imagine how much it means to me to hear that from you, from true Viola fans!"
Barák also paid tribute to two figures closely associated with the club during his time there, former general manager Joe Barone and former owner Rocco Commisso, both of whom passed away during his spell in Florence.
"During my journey at this club, we sadly lost two people who gave me everything: JOE BARONE and ROCCO COMMISSO. Two people who, through their human values, represented this club that I love in the best possible way," he wrote.
"Saying thank you isn't enough — I wish I could give them so much more. I will always be grateful, and they will always have an important place in my heart! The only sporting regret is not being able to lift a trophy with you, because the Fiorentina fans deserve it as much as anyone. Three lost finals in two years bother me, but in the end other things matter more in life, and you gave me far more than winning a final would have.
"With happiness and tears in my eyes, I say goodbye and wish you all the best! I will never forget the Viola people! Thank you so much! Yours, Tony."