Johnson, who was part of three NBA champions, two with the Boston Celtics and one with the Seattle SuperSonics, had been coaching the Austin Toros of the NBA Developmental League.
The cause of death is not known.
"He will be autopsied," said Mayra Freeman, a spokeswoman for the Travis County Medical Examiner's Office.
Johnson was the MVP of the 1979 NBA Finals, averaging 22.6 points as the Sonics beat the Washington Bullets in five games.
After a brief stint with the Phoenix Suns, Johnson rejoined the Celtics, where he teamed with Larry Bird, Kevin McHale, Danny Ainge and Robert Parish for a glorious run in the 1980s that saw Boston win the 1984 and 1986 NBA championships.
UPDATE: An impressive outpouring of Dennis Johnson thoughts and memories on ESPN.com. You can add your own, too.