Mourinho said that the experience of Schwarzer, who joined on a free transfer after leaving Fulham, will ensure that his goalkeepers remain competitive.
"Mark is what we need," Sky Sports News quotes Mourinho as saying. "I always thought, even when I was not at Chelsea, that we have we have the best keeper in the world in Petr.
"But we need competition for him, motivation for him, security and I think Schwarzer is perfect for that.
"He has experience, has spent his whole career in the Premier League, so it's his national habitat. Getting Mark on a free transfer, we have the goalkeeper to complete our set of goalkeepers."
Before his time at Fulham, Schwarzer played for Middlesbrough.