The 35-year-old Uruguayan, formerly of Ajax, Liverpool and Barcelona, is being released by Atletico at the end of his two-year contract.
His second season has not delivered to the same level as his first, where his 21 league goals drove Atletico to the LaLiga title, and the club see this as an appropriate time to part ways.
Suarez started Monday's (AEST) home game against Sevilla, which ended in a 1-1 draw after the visitor snatched a late equaliser.
He could not grab a goal to mark the occasion, after Atletico confirmed prior to kick-off it would be his last game for the club, and Suarez was clearly emotional when substituted midway through the second half.
Head coach Simeone paid tribute, and there was a guard of honour for Suarez and midfielder Hector Herrera after the final whistle, as Atletico's players marked the exits of both players.
Simeone said his chief thought regarding Suarez was "gratitude", after the player who remains the third-highest scorer in Barcelona's history signed off from his stint at the Wanda Metropolitano.
"He came to try to remain at the top, to show how competitive he is," Simeone said. "He helped us, and we helped him to win LaLiga where he was decisive due to his forcefulness. This season, despite not playing the games he would have wanted, he is still the team's top scorer.
"I wish him the best, with absolute gratitude to an extraordinary footballer and to a person who goes beyond a footballer."
Jose Gimenez headed Atletico ahead after 30 minutes against Sevilla, with an 85th-minute leveller from Youssef En-Nesyri enough to secure Champions League football for Sevilla next season, with Atletico having already made sure.
Simeone's third-placed team have been left behind by Real Madrid and Barcelona this season, and he said his players "need to improve, talk and believe in what we believe in to compete well".
He warned that although Atletico have shown they can be competitive against the big two in Spain, the likes of Sevilla, Real Betis and Athletic Bilbao are also in pursuit of the Rojiblancos.
Looking at what comes next, Simeone said it was important to move on from this season and begin afresh.
"Calm down and, as always," he said, "we will be here."