The former Manchester City manager, who recently left Chinese Super League club Hebei China Fortune, has signed a three-year deal as West Ham boss, succeeding David Moyes at the helm.
Now the 64-year-old will set to work on dragging West Ham back up the Premier League table following this season's 13th-place finish.
"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," said Pellegrini.
"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.
"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."
Former Manchester United boss Moyes replaced Slaven Bilic in November and led the Hammers away from the relegation zone.
But West Ham's board quickly opted not to retain the Scot's services and have now installed Pellegrini instead.
The Hammers' new Chilean boss led Manchester City to the Premier League title in 2014, with the Citizens blasting a record 151 goals in all competitions that season.
Pellegrini believes he shares a common vision for West Ham's future with the club's joint chairman David Sullivan.
"Every time I spoke with the owner Mr Sullivan, I always had the feeling that he wants me," Pellegrini told West Ham's official club website.
"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."