The Emirates club parted with £22million to sign Torreira from Sampdoria after the Uruguay international impressed massively at the World Cup.
"When he called me, I could not believe it," Torreira told Ovacion. "I was in a hotel with a friend, and I got nervous. It was difficult for me to talk because receiving the call from a coach of such an important team generates many things.
"We spoke about several things. He also did not want to fill my head with a lot of things because I knew the World Cup was coming and that I was focused on that."
Upon joining Arsenal, Torreira added: "I feel very happy. I want to make the most of this opportunity life has given me. I am really and looking forward to starting this new adventure.
"I feel calm. I am used to coping with this kind of thing in the best possible way. It's a very positive thing that people want to welcome me.
"It makes me feel comfortable. Now I am calm and I look forward to the future, which for sure will be very nice."