The 26-year-old underwent a medical in London on Thursday night and has completed a move for a reported initial fee of £7.5 million, rising up to £10.75m.
The winger has signed a five-year deal with an option of a further 12 months and becomes the Hammers' record signing.
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Goal.com exclusively revealed last week that West Ham were planning a new approach after an other of £5.5m up front, with a further £4.5m in add-ons, was rejected earlier in August.
Jarvis is expected to go straight into the squad ahead of their trip to Swansea on Saturday lunchtime.
Allardyce has already added several names to the West Ham squad as he aims to re-establish the east London club in the Premier League
On Thursday he told The Daily Mail: “From my point of view it is a big piece of business. I think a quality young man who has got a lot of qualities that will add to the team we have already got.
“When you are trying to create in the Premier League and score goals, he is one of those players who can certainly give defences a really hard time and that is what we are hoping he can do for us.”
Jarvis spent five seasons at Molineux and scored eight times in the Premier League last term despite Wolves’ relegation, and earned his first and only England cap against Ghana in March 2011.