The 20-year-old is regarded as one of the hottest properties in the Swiss Super League, and has netted eight goals in 18 games for the Zurich side during the current campaign.
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.
'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,' the 42-year-old Spaniard added.
'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.
Meanwhile, while speaking to evertontv, Tarashaj said: 'It is a dream for me to play here in Everton; to sign here I am proud and happy to be here.'
Asked to describe himself as a player, he said: 'It's difficult. I'm forced to have a good shot and I think I can help Everton.'
Sportsmail noted in December that he was valued at around £3million, with the club opening talks with Grasshoppers and the young striker at the end of last year.
The player watched Everton's 4-3 defeat by Stoke City with his advisers on December 29.