After returning to Scotland this weekend, Kennedy arrived on Merseyside on Monday.
He told evertontv: "I first found out before pre-season [about Everton's interest] but it was nothing serious. It wasn't until the last week that there's been more and more interest.
"I got up on Friday morning, went to training, didn't know what was going on, didn't think I was going to be an Everton player by the end of the day. But it's brilliant for myself to get it over and done with and I can't wait to get started now."