Solomon has signed a five-year contract that will last until the summer of 2028.
The 23-year-old spent last season on loan at Fulham from the Ukrainian side and scored five goals in 24 appearances.
Foreign players in the Ukrainian league had their contracts temporarily suspended by FIFA following the country's invasion by Russia, which allowed Solomon to leave the country and sign for another club.
Shakhtar have expressed their dissatisfaction with the ruling which prevents them from receiving a transfer fee for their foreign players still under contract.
Solomon is the third new arrival at Tottenham this summer after goalkeeper Guglielmo Vicario from Empoli and James Maddison from relegated Leicester City.
Shortly after his contract was signed, Solomon posted on Twitter: "I'm so delighted and excited to be joining this fantastic football club. It's truly an honour to be here and I can't wait to get started."
Tottenham are looking to kick on under new manager Ange Postecoglou next season after a disappointing eighth place finish in the 2022/2023 season.
Solomon has won 35 caps for Israel, scoring seven goals.
