The agency said the 30-year-old hid income earned in 2014 from a sponsorship deal signed with Adidas shortly before he joined Chelsea from Atletico that year. Costa, who has both Brazilian and Spanish citizenship, returned to Atletico in 2018.
Under a deal with Spain's tax office, Costa will plead guilty to tax evasion and pay €1.1 million in back taxes, daily newspaper El Mundo, reported.
He will also be sentenced to six months in jail but will not serve time and instead pay a fine of €600,000 the paper said. The agreement will be made official at a Madrid court on October 4, El Mundo reported.
Contacted by AFP, a spokesman for the tax office, said he could not comment on individual tax files.
Costa is the latest famous footballers to have fallen foul of Spain's tax authorities.
A Spanish court in January handed Portuguese striker Cristiano Ronaldo a suspended two-year prison sentence for committing tax fraud when he was at Real Madrid.
The player, who joined Italian side Juventus last year, also agreed to pay €18.8 million in fines and back taxes to settle the case, according to judicial sources.
Barcelona's Lionel Messi paid a two-million-euro fine in 2016 in his own tax wrangle and received a 21-month jail term.
The prison sentence was later reduced to a further fine of €252,000, equivalent to €400 per day of the original term.