Simpson moved to QPR last week on a Bosman.
He told nufc.co.uk: "I came at 22 and it's been a big part of my career; not just my career but my life as well with my little one being born here.
"From walking in as a 22-year-old to leaving now, I've matured a lot and changed a lot. Being in Newcastle and being around certain people - team-mates, coaches, managers - and playing in front of those fans has helped me a lot and I'm well happy with the four years.
"Obviously winning the Championship the way we did is one of the highlights, getting back into the Premier League, but also just cementing my place in the team the season before last and finishing fifth.
"And there were one-off games - beating Sunderland 5-1, the comeback against Arsenal... I'll never forget those days and those games, but the whole four years have been top class."