Anderson, 25, has become the seventh deal for the Premier League side since the arrival of their new Chilean coach Manuel Pellegrini at the end of May, reports Efe.
"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," the Brazil midfielder said.
"I'm really happy to be here. It's a dream come true," he added.
Anderson, who scored eight goals and made 10 assists in 32 matches with Lazio in the 2017/2018 season, did not rule out becoming "a legend" in the English club like Moore, Tevez and Di Canio.
"They were great players and idols here, and I'm aiming big - who knows? Maybe I could hit their heights," he said.
Media reports have put the initial signing at 38 million euros ($44.5 million), and while West Ham did not officially announce the figure, it did confirm it had paid a club-record amount.
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