Shani Tarashaj, the exciting Swiss Under-21 international, has signed a four-and-a-half year deal with the Club to June 2020.
Regarded as one of Switzerland's most talented, emerging prospects, the 20-year-old has scored eight goals in 18 games for Grasshopper Club Zurich this season.
He will be loaned back to Grasshopper for the remainder of the season, a condition of the transfer which allows him to complete his national service.
Roberto Martinez said: "Shani is an enormous young talent in Swiss football who, without a doubt, will have a great future. We’re delighted to have found a young player who believes that our Club is the perfect step for him to enhance his quality and to grow his career.
“He fits in really well to our style and the way we want to play the game. He is a family boy, hungry and he is desperate to fight for his place in our talented young squad.
“I’m delighted we have been able to act quickly and secure the deal for Shani which means that, due to his national service commitments, he will be able to be part of our first team squad from next season.
“Grasshopper have been very professional and the deal has been conducted in an exemplary way.”
Tarashaj said to evertontv: "It is a dream for me to sign here at Everton. I am proud and so happy to be here.”