He impressed on his return to Arsenal last season but the 34-cap England worldwide was unable to force his way into the squad for the World Cup.
"It feels good, it feels special", said Wilshere, whose father and brother are also lifelong Hammers.
However, Wilshere admitted on Monday that he supported the Hammers as a boy and talked about the "special bond" that he had with the club while he was growing up.
"My family and a few of my friends are West Ham fans so everyone's buzzing".
"The fans, of course - everyone knows how big West Ham's fanbase is - and especially in this new Stadium".
Do you think Wilshere made the right decision to join West Ham?
The same report says that West Ham United are also keen on a deal to land the Brazilian attacker this summer as the Hammers look to strengthen their own squad.
Despite the delay West Ham are confident that Anderson will sign for them with the fee nearly twice their previous record which stands at the £24 million they paid Stoke City last summer for Marko Arnautovic.
There were talks of him going to Turkey but Wilshere has chose to stay in the Premier League and sign a three year contract.
"He's only 25/26, still got plenty of game time in him and I hope he does well".
Wilshere is set to fly to Switzerland to link up with new West Ham manager Manuel Pellegrini's squad at the club's pre-season training camp.
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