The 33-year-old Dutchman has been signed as a free agent after leaving Marseille during the summer.
The Black Cats are now awaiting international clearance to allow Zenden, who has 54 senior international caps, to go into the squad for Saturday's Barclays Premier League clash with Liverpool.
Manager Steve Bruce told the club's official website: "We are delighted to be able to add a player of Bolo's quality to the squad.
"He has performed at the highest level year after year and he's done extremely well during his time training with the club.
"The move happened fairly quickly. Bolo came in and it was immediately obvious that he was still supremely fit.
"Bolo's performances in training have persuaded me that he has a valuable role to play this season.
"He brings international class, a steadying influence and a wide breadth of experience.
"His career is a testament to his quality and he gives us more depth in midfield which is a vital position."