The 33-year-old Dutchman, who has signed a deal until the end of the season, has been included in the squad after receiving international clearance.
Sunderland submitted their documentation before the noon deadline and later received confirmation that Zenden is eligible to play.
Zenden, who was out of contract at Marseille at the end of last season, will now hope to play a part in the match at the Stadium of Light.
He said: "Who knows? I could get my first minutes against my former team Liverpool, which would be something special.
"I am definitely looking forward to that. It's obviously a club that is going places. Since the summer, there is a positive vibe. The club struggled a bit last year, but looking at the squad, if we can finish in the top 10, and there is always a possibility to qualify for Europe as well if you do well in a cup.
"It's hard to say now because you always have to look at where you are after December. When January comes, you get a better look at the situation. But as it stands, Sunderland have had a very good start and if we can continue that way, then definitely we can go places."
Sunderland manager Steve Bruce handed the former PSV Eindhoven, Barcelona, Chelsea, Middlesbrough and Liverpool player a contract after he impressed while training with the Black Cats during the international break.
Bruce said: "He is technically very, very good - you don't play for Barcelona and Liverpool and Marseille and Chelsea and all of those teams if you haven't got really good ability. That was never in question.
"He will give us that little bit of experience, that know-how, and also around the dressing room with the younger lads too, he is everything I hoped he would be."