Depay will sign a contract until the end of the 2022-2023 season, a statement from the club read.
The former Manchester United forward will play again under fellow Dutchman Ronald Koeman, who brought him into the Netheralands set-up after seeing his displays for Lyon, where he moved to from United in 2017.
Depay was the top scorer in the Eredivisie in 2014-2015, his highest scoring season to date. He came close to matching that tally this season for Lyon, scoring 20 times and finishing second on the Ligue 1 charts behind Paris Saint-Germain star Kylian Mbappe, who scored 27.
Netherlands is currently playing at UEFA Euro 2020, with Depay a key element of the team. He scored a penaltyin the 2-0 win over Austria that secured the Oranje's place in the Round of 16.