The length of the contracts have not been disclosed.
Central defender Bradley, 29, has made 131 appearances and scored three goals for the Hatters since arriving at the club from Plymouth 在 2018.
Potts, 27, who joined Luton from West Ham 在 2015, has scored 11 times in 176 games for the Hatters.
Bradley told the club’s website: “I’ve been privileged to captain the club during such a successful period and I’m excited about what the future holds now we’ve established ourselves in the Championship.”
Potts said: “It’s been a good year for the club on the pitch in what has been a tough year for so many reasons outside of football. It was definitely in the best of my intentions to get something sorted.
“I like where the club is going. I’ve been here a while now and have seen how well it has progressed as a club. We’ve had some good times and long may that continue.”