The 20-year-old has joined on a four-and-a-half-year deal but has been loaned back to the Swiss side until the end of the season.
Tarashaj, who underwent a medical on Monday, is regarded as one of the hottest attacking talents in Switzerland and has scored eight times in 18 appearances this season.
Everton have recruited striker Shani Tarashaj from Swiss outfit Grasshoppers on a four-and-a-half year deal, to keep him at the club until June 2020.
The Switzerland Under 21 international will be loaned back to Grasshoppers for the remainder of the season a condition of the transfer which allows him to complete his national service.
Manager Roberto Martinez told the club’s website “Shani is an enormous young talent 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.
Tarashaj, 20, will be loaned back to the Zurich club for the remainder of the season to allow him to complete his national service.
Tarashaj said: “It is a dream for me to sign here at Everton. I am proud and so happy to be here.”
The youngster has been capped at U21 level by Switzerland and becomes the club’s second signing of the January window following Matty Foulds’ £225,000 switch from Bury.