Colombia winger Cuadrado completed a much-anticipated move from Serie A team Fiorentina to Stamford Bridge on Monday, putting pen to paper on a four-and-a-half-year deal.
The 26-year-old, who replaces Andre Schurrle in the Chelsea squad after the German World Cup winner returned to his homeland to join Wolfsburg, is relishing getting to work under Mourinho and becoming part of a team that leads the Premier League by five points with 15 games remaining this season.
Cuadrado told Chelsea TV: "It is really going to be brilliant to work with one of the best coaches anywhere in the world.
"I'm very proud to be playing for him and I think he is going to help me grow into a better player.
"I'm a quick and positive player and I hope to show that on the field of play and help all of my teammates."
Cuadrado has five goals in 37 appearances for his country and now has his sights firmly set on collecting medals at club level.
"We are a big club, so [my target is] winning important things," he added.
"Playing for this team, the league championship is I think the most important thing. As for everything else, Chelsea have big players so we want to win big things."
