Johnston's connections with the University of Washington (where he had carried out his masters and doctoral research) are remembered by a memorial fund that established an endowed graduate-level fellowship within what is now the department of Earth and Space Sciences. By the time of the first anniversary of his death, the fund had exceeded $30,000. Known as the 'David A. Johnston Memorial Fellowship for Research Excellence', a number of awards of this fellowship have been made over the years since it was launched.