It is understood the Black Cats have paid a fee in the region of £8million for the 27-year-old, who can play on the wing or as a forward.
He is reunited with head coach Dick Advocaat, having previously played under him at PSV Eindhoven and AZ Alkmaar.
Advocaat said: “We have signed an international player and I am delighted to welcome him to Sunderland.
“He is a very well-known player in Europe and has played over 30 games for the Dutch national side, which shows his calibre.
“I have worked with him twice already, at PSV and AZ, so I know him well; he is fast and he has scored goals everywhere he has played so that will help the team.”
Lens brings experience of both the Champions League and Europa League to the Stadium of Light, and also has a number of honours to his name, having won the Eredivisie with AZ in 2009, the KNVB Cup with PSV in 2012 and the Ukrainian Premier League with Dynamo this past season.
Black Cats sporting director Lee Congerton said: “We’re absolutely delighted to sign a player of Jeremain’s quality, who has Champions League experience and is a regular for Holland, one of the world’s strongest national teams.
“He’s a direct and quick player with or without the ball and those characteristics are something we’ve been lacking as a side.”
Lens’ arrival completes a mixed day for Sunderland in the transfer market as they saw a move for Zenit St Petersburg defender Nicolas Lombaerts fall through.
Sources close to the club have indicated that the deal fell apart because of an issue picked up by medics.
Rumours that the 30-year-old Belgium international had failed a medical began to circulate on Tuesday evening, and it is understood that a proposed £5million transfer has now been put on hold.