The 25-year-old has signed a three-year contract with Reading and joins the club on a free, as his contract with the Magpies has expired.
He told Reading's official website: "It feels brilliant to have signed, it is a great honour and I am very excited.
"As soon as I met the manager and (Director of Football) Nick Hammond my mind was made up, it was a no-brainer. Reading is a fantastic family club and I'm so excited to be part of something special for this club."
Reading boss Brian McDermott said: "We're delighted Danny has signed for us. He's brings good experience at a good age, he has real ability to pass the ball, he's got energy, he's hungry and is what Reading is all about.
"We're looking to add players who we think will be good for us over a number of years, not just next season, adding to the players who have already done fantastically well for us."