Spanish outlet El Mundo reports the Brazilian forward pleaded guilty to a tax offense amounting to €1.1m.
He is accused of defrauding the state of more than £900,000 by not declaring payments of more than €5.15m (£4.63m) after his move to Chelsea in 2014.
The tax agency denounced Costa for defrauding the authorities regarding €1m (£890,000) in image rights.
The Spanish treasury added another fiscal crime to Costa before withdrawing and halving the fine.
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Costa is said to have asked Atletico to pay the fee, which they refused.
However, they did give the striker an advance on his wages, meaning he could pay the fine in full. The fee is said to be around €500,000 (£450,000).
Costa was called to testify in June last year, acknowledging the charges put against him.
The 31-year-old was spotted arriving in court today for a short period of time, donning a protective face mask.
An Atletico spokesman said on Wednesday: “Diego Costa reached an agreement a few months ago with the prosecutor and has already paid the corresponding fine plus interest and the request for a prison sentence was withdrawn.
“This week it is expected that agreement will be ratified in court, as is mandatory.”
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Costa’s Chelsea stint ended in tears after a public fallout with Antonio Conte.
Reflecting on his time working with Conte at Stamford Bridge, Costa told ESPN: “[Conte and I] had problems off the pitch, but I think he is a really good manager.
“I have no hard feelings towards Conte, but to be a top, top manager, he needs to change the human side of his management. He is very suspicious. At a team like, say, Real Madrid, he would never last a season.”