The 53-year-old Dyson, who played 30 Tests and 29 one-dayers between 1977 and 1984, coached Sri Lanka for nearly two years from 2003.
"The rest of the team management will be identified and appointed subsequently," the Web site added without saying when Dyson will start in his new role.
Dyson succeeds fellow Australian David Moore, who was coach on a temporary basis after Bennett King quit following the 50-over World Cup in March.
