The 49-year-old leaves his job with Blackpool to take the reins at Selhurst Park on a four-and-a-half-year deal, following former boss Dougie Freedman's departure for Bolton
Steve Parish, the London club's chairman, had confirmed to the BBC on Friday that an approach had been made for the Tangerines boss and the switch has now been made official, the 49-year-old signing a four-and-a-half-year contract.
Holloway was unhappy with his rolling contract with Blackpool and made clear that he wanted a more secure deal for himself.
He told reporters days before his departure: "Will I be the Blackpool manager for the rest of my life? No, I can't see that happening."
"I wish Ian all the best in his new role," Blackpool's majority shareholder Owen Oyston told BBC Radio Lancashire.
"He has done a fantastic job for us during his time here and will be remembered as the most successful manager in the club's history.
"Things happen in football very quickly, as in this case, so I am not shocked by his decision. It suits him to be nearer his family and I am sure he will enjoy the new challenge he has set himself.
"There is no animosity, he goes with my best wishes having served our club so well and the success he brought to the club during his three years here.
"Steve Thompson will take charge of the team at Derby this afternoon. I will then be making an appointment as soon as possible."
Blackpool 's head of coaching Keith Millen also followed Holloway out of Bloomfield Road, taking up the assistant manager's position at Selhurst Park.
Holloway left the seasiders after three years at the club which included promotion to the Premier League via the play-offs in 2010.