Hennessey, aside from a few loan deal including last season at Yeovil Town, has spent his entire career at Wolves and was "delighted" with the deal to take him to the Premier League.
"I'm delighted to be here, I've met some of the lads and the staff already so I'm just looking forward to getting out onto the training pitch now," he told the club's official website. "We've got Arsenal on the weekend which is going to be a tough game but hopefully we can get something out of it.
"I know Danny Gabbidon well and he's been telling me what the place is all about. He said it's a fantastic club and that I should get down here so I'm over the moon it's happened.
"Going out to Yeovil was good for me as I managed to get match experience again but then that came to an end and I went back to Wolves and was sadly on the bench. Hopefully the tables will turn for me now."
Hennessey made 152 league appearances during his time at Wolves.