The former England international has joined Spurs on a free transfer after being released by Burnley.
"I've got huge admiration for Hugo, one of the world's greatest goalkeepers," Hart told Tottenham's official website.
"I'm genuinely really excited to work with him, excited to push him, excited to learn from him."
On Mourinho, Hart added: "He's done huge things in the game. I've always had a good relationship when playing against him.
"We've always found a way to come together and discuss the game and I think we can really work together as a team, work together as a unit."