The 26-year-old had not made an appearance for the Royals in the Championship this season, amid speculation that he was keen to leave the Madejski Stadium.
An agreement has been reached with Palace over personal terms and he has successfully come through a medical examination in south London.
He told the Palace website: "I'm delighted to be joining Palace and playing in the Premier League again. It's something everyone dreams of doing.
"Playing there last season was a great challenge as it is the biggest league in the world and you're playing against the best players, so when this opportunity came to me I jumped at it.
"Selhurst Park is always a great place to play, the atmosphere has always been amazing and I've had some great games against this club."
A Reading statement said: "The club would like to wish Adrian the best for the future and thank him for his efforts and contribution."
The defender joined Reading in 2012, having previously spent seven years at Watford, and played 31 times for the Berkshire club last season.