Keen to avoid immediate relegation back to the Championship, Eagles manager Tony Pulis made five signings on the final day of the transfer window.
Scott Dann arrived from Blackburn for an undisclosed fee on a three-and-a-half year deal as the deadline approached, before late confirmation came through of the arrivals of Ince and Ledley.
England Under-21s winger Ince has moved to Palace on loan until the end of the season, when his contract with Blackpool expires.
Ledley's contract was also up in the summer and the Wales international has swapped Celtic for south London, signing a three-and-a-half year deal.
Hennessey said on Palace Player: "I have met some of the lads and the staff already, so I am just looking forward to getting out onto the training pitch now.
"We have got Arsenal on the weekend which is going to be a tough game but hopefully we can get something out of it.
"I know (defender) Danny Gabbidon well and he has 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 am over the moon it's happened.
"Going out to Yeovil (on loan) 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."
Puncheon, who was at the Selhurst Park club as a youngster, said: "It is great to sign a permanent deal, it's something I dreamt about when I was a kid so I'm pleased to get it done.
"The massive factor in this was the chairman and the manager, the gaffer has shown great faith in me since he has been here and that's been unbelievable for me.
"It is a boost for me mentally - I thought it might happen at the end of the season, but it has come quicker and obviously that is good for both me and the football club."
Palace also confirmed on Friday afternoon that Jose Campana has been loaned out to Nurnburg.