Witsel moves to Atletico as a free agent after coming off contract at Borussia Dortmund last week.
The Belgium international has signed a one-year contract with Atletico.
Witsel said, "For me Atletico is a great club and I would like to stay here at a top level, playing the Champions League. I'm here for that.
"Cholo Simeone is one of the best coaches in the world, I can't wait to work with him.
"I spoke to (Yannick) Carrasco last week, he told me very good things about this club and I'm very happy to be here. I came to play here at the time of Zenit, I found a 'local' environment, the people were incredible.
"I can't wait to work and play in this stadium and feel this warm environment."