The full-back, who was expected to leave St James' Park after failing to agree a new deal with the Magpies, has become manager Harry Redknapp's first signing of the summer.
"I want to play week in week out," Simpson told the club's official website. "That was the main thing for me. Harry wants me playing and he wants me involved. He's a top manager, and as soon as I spoke to him I knew this was the right move for me.
"From what I have heard from Harry and the staff I have spoken to, along with some of the players here who I know well, they are very determined to put things behind them and start afresh and get back into the Premier League where the club belongs. I want to play my part in that and do everything I can for the club and the fans. I really think we can go straight back up."
Redknapp added: "He's the type we want at the club. He's a good professional, a good character and a good player who knows his job in the side. He'll be a really fine acquisition for us. It's a fantastic piece of business for the club on a free transfer."
Redknapp failed to secure his first target when Reading snapped up Wayne Bridge from Brighton & Hove Albion.