The Netherlands international has caught the eye in the Eredivisie over recent seasons and attracted further attention after impressing at the World Cup in Brazil.
Amid reported interest from Manchester United, Juventus and Tottenham, Depay has put pen to paper on a one-year extension.
The 20-year-old has scored four times in two league games this season and the in-form Dutchman his pleasure at agreeing his new deal.
"I want to develop myself in this team, which last season set off on a path to success," he explained to the club's official website.
"I want to play for prizes and make myself important to the team.
"I am pleased that we have reached a breakthrough and extended my contract with the club."
Technical director Marcel Brands added his delight at finalising talks.
"Behind the scenes, we have worked hard to keep Memphis in Eindhoven," he said.
"We are more than pleased that he has entered into this new commitment."
