Wilshere turned down the offer of a new Arsenal contract after Wenger stepped down at the end of last season, saying he had not been guaranteed regular playing time by new boss Unai Emery.
"It feels special. Many people know that I've had a special bond with this club growing up", he said.
Speaking after signing for West Ham, the 26-year-old said he feels good joining his childhood club.
"He makes me think of Mbappe because I played him at 17 years of age as he was an exceptional talent". "The manager [convinced me],..."
"The fans, of course - everyone knows how big West Ham's fanbase is - and especially in this new stadium".
In an interview, Wilshere claims his entire family were Hammers' fans and he had one specific player on the back of his shirt.
Versatile attacker Felipe Anderson, meanwhile, has been a target of Manuel Pellegrini's since he took the West Ham job, and the deal finally appears to be gaining traction after previously reaching something of an impasse.
"Jack is a player with excellent technical ability, combined with great energy and commitment, and has proven his quality both in the Premier League and at worldwide level", he told the club's website.
Now, after completing his move to West Ham United from Arsenal, Wilshere has spoken of his delight at sealing the transfer.
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.
Last season he made just 12 starts for Arsenal in the Premier League, also making the same amount of starts in the Europa League.