The former Scotland and Norwich defender, who joined the club as a player in January and has made 16 appearances this season, will take charge with immediate effect.
The Dons are in the relegation zone in Sky Bet League One, having lost eight of their last nine games, and parted company with Tisdale following Saturday's 3-1 defeat to Tranmere.
Martin's first game in charge will be the FA Cup first-round clash with Port Vale next weekend.
The 33-year-old told the club's official website: "I'm excited and proud to have been given this opportunity to become manager of MK Dons. Football management is something that I've been preparing for for a long time, and this is an opportunity I'm ready to take on.
"I would like to thank Paul Tisdale for bringing me to the football club and for his hard work during my time here."
Martin has played in all four divisions in England, as well as the Scottish Premiership with Rangers, and the Dons said he is currently completing his UEFA Pro Licence and the League Managers Association's diploma in football management course.
MK Dons chairman Pete Winkelman said: "Ever since Russell joined the club, we recognised his potential to one day become a manager.
"It's certainly happening faster than we expected but I'm excited to give Russell the chance and show us all what we can do.
"He's taking over the club mid-season and faces an immediate challenge given recent form, but we have great confidence in his ability to turn this season's fortunes around and head the club back in the right direction."