The club announced the deal via their official Twitter account, as Pellegrini put pen to paper on a three-year deal:
"I am excited about this project," Pellegrini told West Ham's official website. "My mentality is always to have a winning mentality and I will hope that I can repeat here what I did with all my clubs here in Europe, where I have always arrived in European competition."
"I know that this league is very good and it’s not easy to do it, but I think that working all together with the owners, the technical staff and the fans, we have an important power and can think about reaching important targets for the season.
"I think West Ham has a very good team. I know all of the players and I saw most of the games that they played last season, so I am sure that, with the players we have in this moment in the squad, and bringing maybe another four or five players in, we are going to have a strong team."
Bleacher Report's Dean Jones gave his take on the appointment:
Joint-chairman David Sullivan gave an indication the club would be backing him in the transfer market.
In a statement accompanying Pellegrini's announcement, Sullivan said "the club believe he will attract new talent to the London Stadium" and that he will soon "get down to shaping the squad he wants."
The 64-year-old departed Hebei China Fortune on Saturday having been with the Chinese club since leaving City in 2016.
Pellegrini is in his 30th year of management and brings with him an impressive CV.
He won three league titles and as many cup competitions in South America, before winning the Premier League in 2014 with City as well as two League Cups.
OptaJoe shared his impressive record in English football:
The Chilean also spent one season with Real Madrid in 2009-10. Although Los Blancos failed to win La Liga that year, they achieved a total of 96 points under Pellegrini, which was a club record at the time.
Hammers fans might be particularly interested in his time at Villarreal and Malaga, who are more comparable in terms of size and stature with the Irons.
Pellegrini guided Malaga to fourth and sixth in his two full seasons there, while in five years with Villarreal, he finished as high as second and never lower than seventh.
West Ham will be hoping he can have a similar impact at the London Stadium. Since they regained their position in the Premier League in 2012, following their relegation a year earlier, they've only managed two top-half finishes.
Reporter and commentator Ian Abrahams told the Alan Brazil Sports Breakfast show on TalkSport that West Ham need to back him in the transfer market to ensure he's a worthwhile appointment:
Pellegrini is perhaps the best coach the Hammers could realistically have hired, so landing him is quite the coup.
His time at Villarreal and Malaga shows his ability to work on limited budgets, which will be useful as the Hammers don't have the resources to compete with England's elite. However, it would be a waste not to take advantage of his presence at the club by failing to back him.