Wilshere will be looking to rebuild his career under Manuel Pellegrini following a frustrating few seasons at the Emirates Stadium.
Wilshere, who has 34 senior caps and two goals, was unable to win a place in England's World Cup squad.
The 26-year-old midfielder ended a 17-year association with boyhood team Arsenal this summer and joins the club he supported as a child.
"It feels good, it feels special", said Wilshere, who grew up as a Hammers fan.
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Chelsea FC have joined West Ham United in the race to sign Felipe Anderson from Lazio this summer, according to reports in the Italian media.
Antonio was restricted to 21 appearances in a stop-start season last time out, and United will consider offers upwards of £15m.
He spent his entire career with Arsenal, apart from loan spells at Bournemouth and Bolton, after joining the Premier League club's youth system as a nine-year-old.
Meanwhile, NAIJ.com had earlier reported Jack Wilshere has confirmed he will quit Arsenal once his current contract with the club expires at the end of this month.