The 45-year-old has a big reputation after success in Portugal with Pacos de Ferreira before leading Shakhtar to the domestic Treble in his first season in Ukraine after replacing club legend Mircea Lucescu.
The former Braga boss, who has won back-to-back league and cup doubles since joining Shakhtar in 2016, said: "I'm very happy".
Moyes signed a short-term deal in November and helped West Ham climb out of relegation trouble to secure a 13th-placed finish but the Scot parted ways with the London outfit on Wednesday.
Joint chairman David Sullivan said the club had left "no stone unturned" in choosing the person they believe is the "right man to take West Ham forward".
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The Scottish coach restored a work ethic that had been lacking at West Ham, including getting the best out of Marko Arnautovic by reinventing him as a lone striker. Their preference is to hire a manager who has worked in the Premier League, although they have not denied making contact with Shakhtar Donetsk's Paulo Fonseca last week. Now everything will go wrong with Shakhtar, there will be problems. Let us know what you think by dropping a comment below.
"And what do we see?"
It was previously reported that "Miners" suggested the coach to extend the contract for two years, but he is waiting for offers from clubs in the English Premier League.
Nonetheless, we now have additionally realized they don't assume the clause which states he should pay a 12 months's wage if he breaks his contract is an impediment to leaving the membership. "He knows what to do".