Hart, 56, will be in control at Selhurst Park until the summer as he bids to keep the club in the Championship. Hart spent time as Rangers boss earlier this season, but quit after less than a month.
"I think it's quite obvious I like a challenge, and this is a big one, but I felt that the support would be there," he said.
"There's only one objective and that is to stay in this division. This club deserves to be in this division, there's been a lot thrown at it in the last six months and the players don't deserve it.”
Former Palace players Dougie Freedman and John Pemberton will join Hart’s backroom staff.