The 26-year-old is Harry Redknapp's first signing of the summer at Loftus Road after being released by Alan Pardew's side at the end of last season
The 26-year-old has signed a three-year contract with the Championship club and is Harry Redknapp's first signing of the summer.
Simpson made 19 Premier League appearances for Alan Pardew's side last season but found it difficult to secure a starting place ahead of Mathieu Debuchy.
“I want to play week in week out. That was the main thing for me. Harry wants me playing and he wants me involved,” Simpson told the club's official website.
“He’s a top manager, and as soon as I spoke to him I knew this was the right move for me. I’ve always admired him. He is a great man in the game and I have a lot of respect for him.
“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."
Redknapp revealed he consulted Newcastle's coaching staff before signing Simpson and has labelled the full-back as a 'fine acquisition'.
“I spoke to a few of the coaching staff at Newcastle – friends of mine from over the years who I know and trust – and they spoke very highly of him," Redknapp said.
“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.”