Atletico had been unable to register new signings in last summer's transfer window after being handed a ban by FIFA for irregularities in relation to the transfers of minors.
But they had already agreed deals to bring Spain striker Costa back to the club from Chelsea and sign winger Vitolo from Sevilla. Both will be able to make their debuts with the winter window opening on Monday.
"I know there is a lot of competition, that they have a lot of goals in them," said Costa, 29, of the prospect of competing with the likes of Antoine Griezmann and Fernando Torres for a starting berth in Diego Simeone's side.
It was in September that Atletico announced the signing of Costa, with Spanish media saying they had agreed to pay Chelsea around 60 million euros ($71.3 million) to bring back a player who starred for them when they won La Liga and reached the Champions League final in 2013/14.
Costa, who has signed a deal through to 2021, scored 20 goals for Chelsea as they won last season's Premier League title but fell out with Antonio Conte, his manager in west London.
Atletico also agreed in the summer to pay the 37.5 million-euro buyout clause to sign Vitolo from Sevilla.
He has spent the first half of this season on loan at Las Palmas although he has recently been sidelined with a thigh injury.
"The injury is behind me. I have spent the last month working with the physios. It's forgotten about now," said the 28-year-old Spain winger.
Atletico, who moved into a new 68,000-seat stadium, the Wanda Metropolitano, at the start of this season, failed to make it out of the Champions League group stage.
However, Simeone's side are the nearest challengers to leaders Barcelona in La Liga, sitting nine points behind in second place with more than half the season still remaining.
They face lower-league Lleida in the Copa del Rey on Wednesday before returning to league action at home to Getafe at the weekend.