Atletico clinched the Spanish league title ahead of fierce rivals Real Madrid with a 2-1 victory over Valladolid at the Jose Zorrilla.
Valladolid drew first blood on the night as Oscar Plano opened the scoring in the first half against Atletico.
However, Simeone's men mounted a successful comeback in the second half as Angel Correa and Luis Suarez both scored to ensure Atletico were crowned champions of Spain.
During Atletico's emotional celebrations at the full-time whistle, Simeone was spotted walking across the pitch to Valladolid defender Kiko Olivas.
The Atletico boss pulled the crestfallen 32-year-old Spaniard to his feet and warmly embraced him with a hug before a pat on the back of the head.
Real fell two points short of Atletico in the title race, despite beating Villarreal 2-1 at the Alfredo Di Stefano Stadium on Saturday.
Spanish newspaper Marca reports that Simeone thanked the Atletico fans for their support amid the impact caused by the coronavirus pandemic.
However, the 51-year-old Argentine manager said that it was "one of the best years to be a champion."
Simeone explained: "I am happy for a lot of people.
"The feelings that come to me is that in such a complex year, with so many people who left us because of the virus, that Atletico come out as champion it is different.
"It has been a difficult year, like all of our history, but it is one of the best years to be a champion."
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