Wright has explained that he is leaving because of his age, as he turned 60 this year, and is aiming to fill his weekends with different activities.
Per BBC Sport, he said that his resignation "had been coming for a while" and had been "fast-tracked" by his age.
He added: "Ultimately, it's time to do a few more different things with my Saturdays. After my debut show whilst still a player in 1997 and many more memorable years, I'll be stepping back from BBC MOTD at the end of this season. I feel very privileged to have had such an incredible run on the most iconic football show in the world."