The 21-year-old was signed by the Toffees in January and will link up with the club for next season.
The Toffees signed the young Swiss star on a four-and-a-half-year deal in January after he had scored eight goals in 18 Swiss league appearances for Grasshopper Zurich in the first half of the season.
Roberto Martinez's side allowed Tarashaj to rejoin with his former club until the end of the season on loan, and since linking up with Grasshopper again two months ago the star has added three more goals to his tally and made his senior debut for the Switzerland national side.
His manager at Zurich, Pierluigi Tami, who previously coached Switzerland's under-21s side and served as Ottmar Hitzfield's assistant for the senior side, is aware that comparisons have been made between the young player and his compatriot, Stoke City star Xherdan Shaqiri.
Having coached both players for the under-21s, Tami likened Tarashaj's talent to that of Shaqiri's but insisted that Everton have bagged the more dangerous player in front of goal.
He told the Liverpool Echo: "Probably Shani has less technical skills than Xherdan Shaqiri but is a better forward with proven scoring ability.
"Shani is very strong at dribbling and in one versus one. Whenever he‘s close to the box, he tries to score. He is a very important player for GC but I’m happy for him. Everton is a great club and it surely is a fantastic step in Shani’s career.
"Shani knows he hasn’t explored his potential yet and that his remaining time at Grasshopper Club Zürich is very important for his start at Everton. Therefore he has been quite successful at keeping his concentration."
Shaqiri has made his name as more of a creative player than a goalscorer, boasting six assists and three goals in his debut season at Stoke, but has still netted 17 goals in 51 appearances for Switzerland.
Any comparison with the former Bayern Munich playmaker is sure to have Everton fans excited as they look for signs that next season will hold better for their side after what looks like it is going to be back-to-back bottom-half finishes.