The 25-year-old winger scored seven goals and provided 12 assists in an injury-hit season for Lazio last term during which he helped the Rome club to the Europa League quarter-finals.
The move has excited West Ham fans as Anderson has proved to be one of Lazio's key players for a number of seasons, having signed from Santos for just £6.75m in 2013.
In 177 appearances across five seasons for Lazio, Anderson has scored 34 goals and provided 42 assists.
West Ham appeared to be close to signing the Brazilian last week after the Gazzetta dello Sport claimed Lazio have already decided what they want to do with the money they receive from the Hammers.
Talk went quiet, though, until last night when a well-placed Italian journalist working for Sky Sports Italy claimed the deal is close after the Hammers included a key clause in a deal worth over £25 million.
Fabrizio Romano, who also writes for The Guardian, said the move is 'so close.
"Felipe Anderson to West Ham, agreement so close!," Romano said on Twitter.
"Last bid from West Ham is €30M (£26.4 million) + 20% future sale: on next hours, Lazio director Tare will be in London to finalize the deal."
The news will excite West Ham fans who look set for a busy summer after the arrival of Director of Football Mario Husillos.