The 38-year-old has made 104 appearances for the club since joining four years ago. He was signed by Tony Mowbray in August 2013 on a short-term deal which was extended by Aitor Karanka following his appointment as head coach.
Konstantopoulos was pivotal to Boro winning promotion back to the Premier League during the 2015/16 campaign, keeping a club record nine successive clean sheets and 22 clean sheets in total.
However, the Greek was behind Victor Valdes and Brad Guzan in the pecking order last season. He will be one of three goalkeepers, along with Connor Ripley and Tomas Mejias, who will begin preparations for next season under new manager Garry Monk next week.