The 27-year-old becomes the first signing for new Eagles manager Tony Pulis, who is expected to further bolster his squad ahead of the deadline with reports of a deal for Blackpool midfielder Tom Ince being talked over.
Hennessey - who came through the ranks as a youngster at Manchester City before joining Wolves' academy in 2003 - will go straight into the squad for Sunday's trip to Barclays Premier League title-chasers Arsenal after agreeing a three-and-a-half year deal at Selhurst Park to provide competition for current Palace number one Julian Speroni.
"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," Hennessey said on Palace Player.
"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."
Meanwhile, Wolves striker Kevin Doyle has linked up with Sky Bet Championship promotion chasers QPR on loan until the end of the season.
The Republic of Ireland international joined Wolves as a Premier League outfit in 2009 but has been plying his trade in League One this term following back-to-back relegations.
He has struggled to command regular first-team starts at Molineux in recent weeks and, following the additions of Leon Clarke and Nouha Dicko, Wanderers head coach Kenny Jackett has opted to let Doyle out on loan.
Having linked up with QPR boss Harry Redknapp, the 30-year-old told the club's official website: "It was all agreed pretty quickly. I jumped at the chance to come here to be honest.
"The club's in a great position for a tilt at promotion and I can't wait to be part of it.
"It was a massive draw to know I'll be part of a promotion push and obviously the manager played a huge role in my decision to come here as well."
BARNSLEY have completed the signing of Arsenal midfielder Emmanuel Frimpong for an undisclosed fee.
The Ghana international has penned a short-term deal at Oakwell until June, 2014.
Frimpong, 22, spent 13 years with the Gunners academy but was limited to just 16 senior appearances at the Emirates. He has also enjoyed loan spells with Wolves, Charlton and Fulham.
BLACKPOOL have signed midfielder Faris Haroun and striker Andy Keogh.
Haroun, 28, joins the club on a short-term contract until the end of the season from Middlesbrough.
Striker Keogh becomes the fifth arrival of Barry Ferguson's caretaker role, signing from Millwall on loan until the end of the season.
BOURNEMOUTH have completed the signing of Charlton striker Yann Kermorgant on a two-and-a-half year deal.
BLACKBURN have signed Cardiff midfielder Craig Conway on a two-and-a-half year deal.
NOTTINGHAM FOREST have re-signed Sunderland midfielder David Vaughan on loan until the end of the season.
PRESTON have signed Bolton striker Craig Davies on loan until the end of the season.
WALSALL have completed the signing of Liverpool striker Michael Ngoo on loan until the end of the season.
BRENTFORD have completed the signing of Oldham defender James Tarkowski on a three-year contract. As part of the deal the 21-year-old will return to Boundary Park on loan when the window re-opens on February 8.
LEYTON ORIENT have signed goalkeeper Ben Alnwick from Charlton and the O's have also completed the signing of midfielder Marvin Bartley on an 18-month deal after he was released by Burnley on Thursday.
NOTTS COUNTY have signed experienced left-back Gareth Roberts while striker Danny Haynes has left Meadow Lane to join Scottish Premier League club Hibernian on loan.
ROTHERHAM have signed Nicky Adams from Crawley for an undisclosed fee.
CRAWLEY have signed Derby goalkeeper Ross Atkins on a month's loan.
Elliott Hewitt has extended his loan stay at GILLINGHAM until the end of the season. The Wales Under-21 right-back has made five appearances for the League One outfit since first joining from Ipswich in November.
Veteran Portsmouth striker David Connolly has joined OXFORD on loan for the rest of the season.
Defender Michael Ihiekwe has extended his loan stay at CHELTENHAM until the end of the campaign.
BURTON have completed the signing of veteran Crawley striker Gary Alexander while the Brewers have also recalled midfielder Jack Dyer from his loan spell at Kidderminster.
ROCHDALE have completed the signing of former Burnley winger George Porter on a short-term deal.
CHESTERFIELD have extended the loan of goalkeeper Ian Dunbavin from Accrington until the end of the season.