The 56-year-old Scot came in as manager in West Ham even during the 2017–2018 season and then saved the football club from relegation.
“It's wonderful to be back. It feels great to come home. I feel very proud to be back here in West Ham, ”Moyes, who has signed on a contract for a year and a half, told West Ham's website.
After 19 out of 38 rounds, West Ham are in 17th place in the English league, a point above the relegation mark. Chilean Pellegrini got fired after Saturday's 1-2 loss at home against the Leicester table.
David Moyes has previously coached Everton and Manchester United. West Ham's next league match is at home against Bournemouth on New Year's Day.