The 28-year-old's departure will be a major blow to the club, who face a fight to hang on to several other key players this summer.
Top scorer in each of his five seasons, Griezmann was the stardust of Atleti, offering spontaneity and craft in a team renowned for discipline and grit.
The 28-year-old Griezmann has a contract until 2023 with Atletico, but has a buy out clause of 120million euros ($134million)
The Argentine coolly dispatched a spot-kick just before half-time, drilling beyond the reach of Jordi Masip after Gerard Pique was bundled to the ground by Valladolid midfielder Michel.
The win was Atletico's first away from home in La Liga in nearly three months.
Luka Modric sees off French World Cup stars to end Lionel Messi, Cristiano Ronaldo grip on Ballon d'Or
Cristiano Ronaldo was second, with France and Atletico Madrid striker Antoine Griezmann completing the podium.
Monaco, which had arrived with no chances of advancing, missed a late penalty as former Atletico forward Radamel Falcao shot wide.
Griezmann's bending effort in the second half looked likely to prove the difference in a contest short on chances at Butarque but Guido Carrillo's 82nd-minute equaliser earned Leganes a deserved point
France coach Didier Deschamps fielded an almost identical team to the one that started the World Cup final, Presnel Kimpembe the lone exception in place of the injured Samuel Umtiti.
One victory from their opening four league games left Atletico seven points adrift of Barcelona a fortnight ago but three on the spin have now steered Diego Simeone's side back on track.
The visitors had fallen behind against the run of play in the 18th minute when winger Samuel Grandsir forced the ball home in a goalmouth scramble after good work from Radamel Falcao.
Griezmann had teased Ramos after Atletico beat Real Madrid 4-2 to win the UEFA Super Cup in August.
Atletico Madrid star Antoine Griezmann says he still can't fathom why he was not voted one of the world's top three players by FIFA.
For Griezmann, who helped Atletico to Europa League glory as well as playing a pivotal role in France's World Cup win, FIFA's choice was unwarranted.
After the month-long drama in Russia, Express picks its team of the tournament. It’s a 4-2-3-1, the most preferred formation this time...