The 27-year-old had spent a spell on loan at Yeovil earlier in the season, but still found himself out-of-favour upon his return to Sky Bet League One promotion hopefuls Wolves.
Hennessey spent his entire career with the Midlands club, but has now penned a three-and-a-half year deal with the Eagles, and is looking forward to a new chapter in his career.
After joining for an undisclosed fee, believes to be £1.75m, Hennessey told Palace Player: "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.
"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."
Meanwhile, Palace have also confirmed that defender Darcy Blake has left the club by mutual consent.
The Wales international made 11 appearances for the Eagles first team after joining from Cardiff in August 2012.
But he suffered a knee injury in December that year and has rarely featured in any match-day squads since.