Moyes was appointed Hammers boss this morning following the sacking of Slaven Bilic less than 24 hours earlier.
West Ham's decision to take things slowly with Moyes comes after the board faced down supporter unrest over his appointment. West Ham is a big club.
Alvaro Arbeloa tweeted "better late than never" as the news broke that the struggling London club had chose to part ways with the manager who guided them to a seventh-placed finish two seasons ago.
West Ham went for Moyes because higher-profile candidates like Carlo Ancelotti, Rafa Benitez and Guus Hiddink did not fancy the job. "I've got no doubts about that, but ultimately we have to show it on the pitch".
Moyes was sacked less than a season into a six-year contract and is still searching for the chance to rebuild his reputation.
West Ham joint chairman David Sullivan said the 54-year-old Scot is "the right man to turn things around".
It is a well-established club, a well-run football club, so I am looking forward to getting my teeth into it and obviously the job is to make sure we get wins and get ourselves up the league.
The Hammers parted company with Bilic on Monday, two days after a chastening 4-1 loss at home to Liverpool convinced co-chairmen David Sullivan and David Gold that the club needed a change of direction to stop the rot.
But Moyes, whose first game in charge will be at Watford a week on Sunday following the global break, urged them to get behind him and his squad.