Dawkins, 52, was a star guard at Duke from 1982 to 1986. He was the coach of the Cardinal for eight seasons, taking the program to the Sweet 16 two years ago.
Stanford went 15-15 this past season and was 8-10 in Pac-12 play, finishing ninth in the conference. The Cardinal were 156-115 in Dawkins' tenure, which ended with an announcement last week that the school and Dawkins were parting ways.
Dawkins replaces Donnie Jones, who was let go earlier in the month after six years with the program.