The transfer could cost Atletico up to an extra one million euros in add-ons.
Barcelona said the deal included an option for them to buy versatile Belgian international Yannick Carrasco from Atletico.
Depay scored 14 goals in 42 matches for Barca after signing for the Catalan giants from Lyon in 2021.
But injury problems and the arrival of Poland striker Robert Lewandowski from Bayern Munich led to Depay only making four appearances for Xavi Hernandez’s men this season.
Depay is the Netherlands’ second highest scorer of all time with 43 goals and netted once at the 2022 World Cup.
He enjoyed a fruitful five-year spell at Lyon after a disappointing stint with Manchester United.
Diego Simeone’s Atletico have struggled this term and are fourth in La Liga, 13 points behind leaders Barca, having also been knocked out of the Champions League.
Depay will be expected to replace Joao Felix who left Madrid earlier this month to join Chelsea on loan.
AFP