The 33-year-old Uruguayan was seen leaving Wednesday's training session in Barcelona with tears in his eyes, and just hours later both clubs announced that a deal was ready.
According to Barcelona, Atlético Madrid will have to pay 6 million euros, equivalent to just over 63 million kronor, for the striker who had one year left on his contract with the Catalan club.
The striker came to Barcelona from Liverpool in 2014 and can look back on six years where his 198 goals - third most in the club's history - contributed to a Champions League title, four league titles and four domestic cup wins.
Earlier in September, there were rumors of a move to Turin and Juventus for Suárez, but this week the Italian big club made it clear instead with Atlético's Alvaro Morata - who Suárez is now replacing.
Suárez is thus the latest player to move since the Dutchman Ronald Koeman took over as coach just over a month ago.
Among others, Ivan Rakitic has left for Sevilla and Arturo Vidal for Inter.
And as recently as Wednesday, Portuguese right-back Nélson Semedo signed for Premier League club Wolverhampton.
A medical examination remains before the deal can be definitively completed, and more details about Suárez's contract with the capital club are not known.
Barcelona states on their website that Luis Suárez will say goodbye to the fans and the club at a video conference on Thursday.
ARCHIVE: Suarez hero for Barcelona against Inter (October 3, 2019)
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Suarez hero for Barcelona against Inter Photo: Emilio Morenatti / AP / TT