Griezmann was understood to be Barca's top transfer target, with a number of club officials openly stating their desire to bring him to Camp Nou during the current transfer window.
The France international was part of a half-hour long documentary broadcast on Spanish TV station Movistar in the buildup to his announcement, and is even thought to have filmed two endings - one saying he will stay at Atletico and one saying he will join Barcelona.
However, Griezmann tweeted his decision at the end of the documentary, revealing that he will stay at the Wanda Metropolitano.
Griezmann is thought to have been offered around £17.5m to stay at the club, in addition to being promised a £100m improvement in the squad this summer.
The 27-year-old has made 209 appearances for Atletico, scoring 112 goals.