0415 GMT July 17, 2019
The 28-year-old World Cup winner has signed a five-year deal which includes an €800 million (£717 million) release clause, BBC reported.
Griezmann joined Atletico from Real Sociedad in 2014 and scored 133 goals in 256 appearances.
He signed a new five-year deal in June 2018 but announced in May he would be leaving the club this summer.
The 2018 World Cup winner becomes the world's sixth most expensive signing behind Neymar, Kylian Mbappe, Philippe Coutinho, Joao Felix and Ousmane Dembele.
Griezmann won the Europa League, the Spanish Super Cup and the UEFA Super Cup during his time at Atletico and was the team's top scorer in each of the last five seasons.
He rejected an offer from Barcelona last year and revealed his thought process in a documentary called ‘The Decision’.
Atletico also reported Barcelona to FIFA over an alleged illegal approach in December 2017.
Griezmann is the third high-profile player to leave Atletico this summer after defender Lucas Hernandez joined Bayern Munich and long-serving captain Diego Godin left to join Inter Milan after his contract expired, while the club has also spent €126 million to buy Felix from Benfica.
Atletico finished second in La Liga last season, nine points behind Griezmann's new club.
Griezmann becomes Barca's fourth major signing of the summer, following the acquisition of midfielder Frenkie de Jong from Ajax, goalkeeper Neto from Valencia and defender Emerson from Brazilian side Atletico-MG.
Griezmann, who finished third in the voting for the Ballon d'Or in 2016 and 2018, joins Lionel Messi, Luis Suarez and Dembele as Barcelona's high-profile forward options.
In addition, Japanese attacking midfielder Hiroki Abe said on Friday he was moving to Barcelona, becoming the second Japanese player in a month to join one of La Liga's big two clubs.
J-League outfit Kashima Antlers, where 20-year-old Abe was spending his third season as a professional, confirmed the move.
Abe is expected to play for Barcelona's B team to start with, Japanese broadcaster NHK said.
The news came as Barcelona prepares to tour Japan later this month for friendly matches, including one against Premier League side Chelsea.
"I felt strongly that I wanted a new challenge at FC Barcelona, although the decision was difficult to make because it required me to leave the team (Antlers) during this ongoing season," Abe said in a statement.
Abe, voted the J-League's Best Young Player last season, was called into Japan's national team for the first time in June for the Copa America where he played in two games, including one as a second-half substitute.
Abe will complete the move after a medical check in Spain, Antlers added.
Abe's transfer comes after Japanese teenage sensation Takefusa Kubo, dubbed the "Japanese Messi", joined Real Madrid last month.