The former Manchester United defender will sign for QPR on July 1, after his Magpies contract came to an end.
The 26-year-old is ready to play his part as the R's look to make a swift return to the Premier League.
"Harry Redknapp is a top manager and as soon as I spoke to him, I knew this was the right move for me," Simpson told the club's official website.
"I've always admired him. He is a great man in the game and I have a lot of respect for him.
"I want to play my part and do everything I can for the club and the fans. I really think we can go straight back up."
Simpson made 137 appearances during his time at Newcastle.