Schurrle became Chelsea's first signing since Mourinho returned as manager at Stamford Bridge when a deal was confirmed earlier this week to bring in the forward from Bayer Leverkusen.
He is aware of Mourinho's reputation as one of the greatest coaches in the world and has already been impressed by the Portuguese boss.
The 22-year-old is now determined to shine and hopes to become a regular in the team, unlike German compatriot Marko Marin - who endured a frustrating first season at the club.
"I first met Jose Mourinho at Michael Ballack's farewell game in Leipzig last week," Schurrle said in The Sun. "He was in charge of my team, the World Select side.
"We met before the game, he shook my hand and told me 'Everything has gone through, and you are my player'. That was a wonderful feeling.
"My first impression of him was that he truly has a special personality. He is a cool guy as well.
"I spoke about him with my national team-mates Sami Khedira and Mesut Ozil, who have played under him for Real Madrid.
"They both told me he is the best coach they have ever worked with.
"I don't fear suffering the same fate as Marko and just being a replacement. I will try to make my way at Chelsea."