The 25-year-old Brazilian attacking midfielder signed for a reported £33.5 million ($44 million, 38 million euros), potentially rising to £42 million, from Italian club Lazio on Sunday.
"We feel he will bring a new dimension to the squad but also complement the attacking players we already have," Pellegrini said.
Anderson was the Hammers' seventh pre-season signing and former Manchester City manager Pellegrini, who took charge of the east London club after they decided against renewing David Moyes's contract, even though the Scot guided them to top-flight survival last season.
"Felipe has a very natural and skilful ability, in the traditional style of Brazilian football, but has proven at Lazio that he also has the strength and mentality to play at the top level in European football," Chilean manager Pellegrini added.
Anderson has joined fellow recruits Ryan Fredericks, Lukasz Fabianski, Issa Diop, Jack Wilshere, Andriy Yarmolenko and Fabian Balbuena at the London Stadium.
West Ham co-chairmen David Gold and David Sullivan, together with vice-chairman Karren Brady, came in for fierce and often abusive criticism from Hammers fans last season but Pellegrini praised club officials for the way they had backed him in the transfer market.
"We are very happy with the players we have signed since I arrived and it gives us a big confidence ahead of the new season," he said.
"The club have made a very big investment this summer and I must thank the owners for their support and backing.
"It has been a very successful week for us with the arrival of four new players, and we look forward to implementing their qualities into our plans and preparations."