Pellegrini’s 18-month spell at the London Stadium was brought to an end following a poor run of results that culminated in a 2-1 home defeat to a second string Leicester City side over the weekend.
West Ham lie in 17th place on the league log, just a point above the relegation zone.
The Hammers have lost 10 of their 19 league games this season, and boast just one win in their last five.
Moyes has signed an 18-month contract and begins his second spell in charge with a home game against Bournemouth on New Year’s Day.
The former Manchester United and Everton manager guided a struggling West Ham side to safety after taking over from Slaven Bilic in November 2017. But his short-term contract was not renewed at the end of the season.
‘It’s fabulous to be back,’ said Moyes.
‘It feels great to be home. I’ve missed being here because I really enjoyed it. I enjoyed being around the stadium and I loved being in this part of the world and I missed the Club, so I can’t wait to get started.
‘I’m feeling very proud that I’m back here at West Ham. But I think more importantly I’ll be looking to see what I can do and what I can make improvements to, how we can get some wins with the players and how we can get some quick wins on the field as well.
‘I do believe that the squad of players I’ve got here is a better squad of players than when I took over before, so I am looking forward to working with them.
‘I think there’s got to be a short-term goal for us just now to get the wins to get us away from the wrong end of the league and what we’re going to do over the next six months, then what we’re going to do over the next period as well. The start is really focusing on the immediate games.’
