Former Manchester City boss Pellegrini left his role with Hebei China Fortune over the weekend and flew to London to seal his return to the English top-flight on a three-year contract.
The Hammers opted not to keep David Moyes after his short-term contract ended following the final game of a Premier League season which saw West Ham pull away from the relegation zone and finish 13th under the Scot.
Pellegrini led City to the Premier League title in 2014, reached the Champions League semi-finals in 2016 and also won two League Cups during his three-year spell in Manchester.
Winning the title with West Ham might be a bridge too far, but the 64-year-old has set his sights on producing an entertaining team capable of exciting fans frustrated by their club's struggles in recent years.
"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," Pellegrini said.
"I always play attacking football and we must try to reach important targets in the season."
Angry about West Ham's move from their historic Upton Park stadium to the London Stadium two years ago, supporters launched furious protests against co-owners David Gold and David Sullivan during a home defeat against Burnley, invading the pitch and throwing missiles at the directors' box.
Pellegrini hopes he can unify the club by signing players who can implement his preferred brand of football.
"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," Pellegrini said.
"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.
"I am excited about this project. 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."
Sullivan hailed Pellegrini's track record with City -- where his team scored 151 goals in all competitions in the 2013-14 season -- as crucial to his chances of ushering in a new era of success at the London Stadium.
"He is one of the world's most respected football coaches and we look forward to working with him," Sullivan said.
"It was important that we appointed someone with knowledge and experience of the Premier League, who already has an understanding -- not only of the teams and players we face -- but of West Ham United and our ambitions.
"Manuel brings a reputation for attacking football and getting the best out of his players. We believe he will attract new talent to the London Stadium as well as improving the current squad."
Pellegrini coached at Villarreal, Real Madrid and Malaga in Spain.
In his lone season at Madrid in 2009-10, Pellegrini failed to win a trophy and was sacked to make way for Jose Mourinho's arrival after finishing second to Barcelona in La Liga.
Pellegrini was in charge when Real signed Cristiano Ronaldo, Karim Benzema and Xabi Alonso, but he blamed the club's obsession with superstars for stopping him building a cohesive team.
He left City in June 2016, to be succeeded by Pep Guardiola, but was soon back in work at Hebei.
Despite being under contract through to the end of 2018 and with a reported release clause of $7 million, Hebei confirmed on Saturday that Pellegrini had left his role.