The deal is thought to be worth an initial £35m, rising to £42m depending on performance-based incentives, and breaks the previous most-expensive transfer fee of £20.5m that was paid for Andre Ayew in Auguest 2016.
The Brazilian has signed a four-year contract to join up with new manager Manuel Pellegrini, and after five years with Serie A side Lazio, he is hoping to establish a name for himself at the London Stadium.
"I feel really happy and fulfilled to join West Ham United," Anderson said. "West Ham is a club with a lot of tradition, lots of great players have played here, like Bobby Moore, Carlos Tevez and Di Canio.
"They were great players and idols here, and I’m aiming big, who knows, maybe I could hit their heights and be a legend here too. I'm really happy to be here. It's a dream come true.
"I want to thank the owner, David Sullivan, because he made a big effort to bring me here. I know how difficult it was, so I have to thank him a lot, and I hope I can repay his faith in me on the pitch with goals and winning games."
The arrival of the 25-year-old is the seventh news signing of the summer, making West Ham the most active club in the Premier League so far. He follows the announcements of Jack Wilshere, Andriy Yarmolenko and Fabian Balbuena in the last week, while the club had already signed Ryan Fredericks, Lukasz Fabianski and Issa Diop earlier in the transfer window.
Anderson will be tasked with increasing West Ham’s threat in front of goal after they struggled to find the back of the net last season, with their director of football Mario Husillos excited by Anderson’s potential having scored eight goals with Lazio last season as well as recording 10 assists across 32 appearances.
"We are very happy and pleased to welcome Felipe to West Ham United," Husillos said.
“We believe that we have signed one of the most exciting talents in European football. Felipe has shown a fantastic level of performance at Lazio in recent seasons and we believe that he will now bring that quality to the Premier League. He is also a player very suited to the style of Manuel Pellegrini.
“For West Ham United this is a very big statement, a club record, so we must thank the owners for their support and work in making this transfer possible.
“It is a negotiation that has taken some time but it is a very good sign that Felipe was determined to become a West Ham player, and we feel very confident that he will become a big success at London Stadium.”
Joint-Chairman David Sullivan added: “Felipe was a main target of the manager so we are delighted we’ve been able to bring him to the club.
“We’re very pleased with the business we’ve done so far and I hope the supporters are just as excited as we are about the squad we are building here at West Ham.
“The deal sees us significantly break our transfer record and we feel it’s a real statement of intent.”
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