The 31-year-old defender featured 49 times in all competitions last season, helping the club win promotion to the Championship.
Speaking to the club’s official website, Beevers said: “We had a lot of success as a group last season, and it is great that so many of last season’s squad have signed new deals.
“Ever since I walked through the door, I was made to feel extremely welcome, and I know that any additions we make in the summer will settle very quickly because of the group that we have here.”
He follows in the footsteps of Christy Pym, Dan Butler, Frankie Kent, Ronnie Edwards, Nathan Thompson and Ricky-Jade Jone,s who all committed to new deals over the summer.
Manager Darren Ferguson said: “I am delighted, we wanted to get Mark tied down on a new deal.
“Since he walked into the building, he has been outstanding, a really good skipper and a great lad to work with. He is good to work with as a manager because you need a captain who can be that go-between when it comes to the relationship between myself and the players.”
The three-year contract will keep Beevers at the club until 2024.