"The agreement between the clubs is complete and will be finalised in the next few hours," Atletico said on their website (www.clubatleticodemadrid.com).
"The midfielder has travelled with the club's permission to join up with the Italian team," they added.
Fiorentina also confirmed the deal and carried a picture of Suarez on their website and footage of his first training session with his new team mates at the New York Red Bulls training facilities in New Jersey on Wednesday.
"There is nothing more difficult than saying goodbye to a place you love and that you feel a part of," Suarez, who will join up with fellow Spaniard Joaquin in Florence, said on his Twitter account (@MarioSuarez4).
"It was a very difficult decision but I feel that it is time to close one chapter and seek new goals," he added.
A graduate of Atletico's academy, Suarez, 28, spent five seasons in the club's first team, during which he helped them win one La Liga title as well as the Europa League, the King's Cup, one Spanish Super Cup and two European Super Cups.
He has made three appearances for Spain, most recently in a friendly defeat against Netherlands in March, but was not included in Vicente del Bosque's most recent squad.
He also had loan spells at Real Valladolid and Celta Vigo and spent two seasons at Real Mallorca before returning to Atletico in July 2010.
(Reporting by Iain Rogers, editing by Toby Davis)
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