The 35-year-old French striker, Atletico's all time top goalscorer, is leaving at the end of the season to join MLS side Orlando City.
Simeone addressed Griezmann directly before a press conference they were giving Tuesday before the clash against Barca at Camp Nou.
"I want to thank you for your work, your humility, and your exemplary attitude for all the kids, in a society that really needs people like you," Simeone told the forward.
"Thank you for everything you've given us, everything you continue to give us... You're a player, but I also consider you a friend.
"We still have a Copa del Rey final, and if God wills it, we’re going to play five more matches in the Champions League. Enjoy it, I care about you a lot."
The coach, known to be extremely demanding with his players' work-rates, joked that Griezmann was not off the hook just because he was leaving.
"That said, I'm still your coach, so you know that tomorrow if you don’t run, you're coming off," said Simeone.
Griezmann, who won the 2018 World Cup with France, thanked Simeone and said it was an "honour" to play for the Argentine.
"I hope people will remember my performances and my efforts. A guy who works hard for the team and who scores goals from time to time," said Griezmann.
However, the forward did not want to speak about his move to the United States, and instead was focused on the clash with his former side Barca, whom he joined for a troubled two-year spell between 2019-2021.
"We know what they’re capable of at home. They're a team that attack very well and defend a bit less well, but their calculations are perfect; if they concede one goal, they score three."