The French international has announced terms on a five year deal, which will earn him €17million (£15m) annually.
Griezmann has finally announced his desire to leave the Wanda Metropolitano, 12 Months after turning down a move to Camp Nou.
His release clause is set to lower on Monday, due to stipulations inserted within his contract.
The World Cup winner previously had a buy-out value of £180m (€200m), which will drop considerably to £107m (€120m).
Atletico manager, Diego Simeone has reportedly asked whether Barca defender, Nelson Semedo could be included in a deal, though the Catalans are not open to the Portuguese defender leaving.