Kardashian had arranged the meeting between West and Wozniak as a surprise birthday and Father's Day gift for the rapper, who recently said he was an admirer of Wozniak and Apple co-founder Steve Jobs, ABC News reported Friday.
Kardashian had given West an Apple Pro Computer mouse signed by Jobs and the arrangement was for Wozniak to sign a second mouse during the meeting.
"It was going to be a big surprise for Kanye," Wozniak told ABC News. "What a beautiful idea from Kim.
"I signed the mouse in front of him," he added. "It's really rare, both our signatures in matching form."
After Jobs died in October 2011, West told The New York Times he believes he's the next Steve Jobs.
"I honestly feel that because Steve has passed, you know, it's like when Biggie passed and Jay-Z was allowed to become Jay-Z ... I will be the leader of a company that ends up being worth billions of dollars, because I got the answers," West said.
Wozniak said he and West talked in the hospital about some business ideas the rapper had.
"It was an excellent conversation for about 2 hours and he finally got into his grandiose business ideas," Wozniak said. "I have some comments to give him. I have been thinking about it since the meeting."