The 26-year-old joins on a 5 year contract and is in line to make his debut in the game against Swansea City this weekend.
Statistics say that Jarvis was the most prolific and accurate winger in the Premier League last season for relegated Wolves and this is believed to be the reason Allardyce has tracked him all summer.
Speaking to the official site Jarvis admitted he was delighted to finally secure a move back to the Premier League.
“I’m delighted to have signed. It’s a fantastic club and I’m pleased to be here. It’s a great club and it’s got great history and tradition. I know about Bobby Moore and the history and tradition that go with that.
“I’ll be playing with some fantastic players and it’ll be great to get into training and I’m looking forward to playing with them. Hopefully I will add a bit of pace, crossing and deliveries that will provide some assists.”