The Ivory Coast international, 23, replaces Idrissa Gueye, who has joined Paris St-Germain for around £30m.
“I've joined a big club like Everton, it's a big moment with a lot of emotion," Gbamin told evertontv. “Now it's on me to prove on the pitch why they bought me.
“I'm excited because Everton is a great club here in England with a big history with ambition so I didn't think for more than a moment - I wanted to come here.
“I can't wait to play at Goodison Park. I'm really excited to start with the team, with everybody. I will, with the help of the manager and all the staff, make myself ready.
“I like to go in the duels. I like to run a lot and tackle. I also pass good and have a good transition. All the rest, fans will see.
“This is my job. I will give everything for the fans on the pitch."
Good evening, Blues... pic.twitter.com/ryZFnKLcNo— Everton (@Everton) August 2, 2019