On Tuesday morning, West Ham confirmed that the Chilean had penned a three-year contract at the club after leaving Hebei China Fortune over the weekend.
The appointment of Pellegrini is a coup for the East London outfit, and the former Manchester City man has spoken highly of the way that he has been welcomed to the club by co-owner David Sullivan.
The 64-year-old told the club's official website: "I'm very happy because I return to a league that, for me, and I always say the same thing, is the best league in the world, and especially because I come here to West Ham because every time I spoke with the owner Mr Sullivan, I always had the feeling that he wants me.
"I think that West Ham had a difficult season last season and I hope that next season we are going to play football that will delight the fans. I always play attacking football and we must try to reach important targets in the season.
"Every time you have a meeting you have feelings about whether it was a good meeting or a bad meeting and I had the meeting with him, just talking about football and talking about West Ham. We agreed on a lot of things he wants for this club in the way I think a football club must be managed, so we have a lot of common ideas."
During the closing months of his stay at Man City, Pellegrini worked in the knowledge that he was going to be replaced by Pep Guardiola at the end of the 2015-16 campaign.