Costa joined Mineiro in August on a free transfer after his second spell at Atletico Madrid ended early.
The 33-year-old made 19 appearances across all competitions for Mineiro, scoring five goals and helped them win the Brazilian league title and the Copa do Brazil.
"Today, officially, I say goodbye to Atletico," he wrote on Instagram.
"I would like to thank all [Atletico Mineiro fans] for all the support and affection I received from the first to the last day.
"Thank you so much for being part of my childhood dream of playing in Brazilian football and winning titles.
"I would also like to express my gratitude to the entire technical staff, medical department, employees and especially to my teammates who helped me daily, always doing everything to make me feel comfortable.
"The feeling that remains is gratitude to all of you Atleticanos. Thank you and I wish you all the success in the world!"
Costa won the La Liga title with Atletico in his first spell at the club and added the Europa League trophy in his second.
Costa’s three-year stint at Chelsea produced two Premier League titles and one League Cup.
Costa was born in Brazil but has represented Spain at international level, winning 24 caps for La Roja and scoring ten goals.
Costa has been linked with a move to Arsenal, who have ostracized top marksman Pierre-Emerick Aubameyang for indiscipline.
