Born in Santa Margarida, a neighborhood in Rio de Janeiro, Deyverson began his career with lowly local side Grêmio Mangaratibense in 2011.

Known as Acosta at the time, he made his senior debut on 10 March 2011, starting and scoring the opener in a 2–0 Campeonato Carioca Série C home win against Duquecaxiense.

On 21 July 2016, after Levante's relegation, Deyverson signed a one-year loan deal with Deportivo Alavés also in the top level, with a buyout clause.

He helped the club lift the 2018 Campeonato Brasileiro Série A by scoring nine goals, but subsequently fell down the packing order after the arrival of Luiz Adriano.

[16] On 27 November 2021, Deyverson scored the winning goal of the Copa Libertadores Final in the 5th minute of extra time, following a defensive error from Flamengo midfielder Andreas Pereira and was elected the Man of the Match.

[23] Three days later, he was named man of the match for scoring a brace in a 2–0 win over Fluminense in the quarter-finals of the Copa Libertadores, helping Atlético revert a 1–0 defeat in the first leg.

[24] On 23 October, Deyverson once again received a Copa Libertadores man of the match award for scoring twice and assisting the third goal in a 3–0 win over River Plate in the first leg of the semi-finals.