The 25-year-old Inter Milan midfielder, a Euro 2016 winner with Portugal, has agreed a loan deal with the Hammers until the end of the season.
And with West Ham decimated by injuries and still firmly in the relegation mix, Moyes desperately needs Mario to adapt quickly to the demands of the Premier League.
“My biggest concern is not him as a footballer but getting used to the Premier League, the speed and competitiveness compared to Italy or Portugal,” said the Hammers boss.
“His ability as a footballer is not in question, he’s proved it, and I just hope he can hit the ground running. That’s my only concern.”
Moyes urgently needed reinforcements to add to his increasingly threadbare squad, with Marko Arnautovic and Manuel Lanzini the latest players to suffer injuries.