Terms of the deal were not announced but local media reported the contract would be worth 70 million Brazilian real ($12.54 million).
The 30-year-old has scored 46 goals in 98 appearances for the Netherlands but was left out of the squad for this month's Nations League matches. Ronald Koeman's side beat Bosnia 5-2 on Saturday and will face Germany on Tuesday.
Depay's international career is far from over, though, with Koeman confirming his transfer to Brazil will not hinder his chances of playing for the national team.
"I disapproved of Steven Bergwijn's move to Saudi. With Memphis it can be different," Koeman told reporters on Monday.
"The level of the league in Brazil is different, so yes, he can still be part of the national team, but it depends on his fitness and if he reaches his level."
Depay began his career at PSV Eindhoven and has had spells with Olympique Lyon, Barcelona and Manchester United. He made 31 appearances in all competitions for Atletico Madrid last season, scoring nine goals.
