Ponder, a native of Australia, selected the Wildcats over South Carolina. He visited both schools.
The Hutchinson Community College standout will join a loaded Arizona class that already ranks among the top three in the country.
To go with Pinder, Miller has signed five-star prospects Terrance Ferguson, Rawle Alkins, Kobi Simmons and Lauri Markkanen.
This past season, Pinder averaged 10.2 points and 6.9 rebounds. Ponder has two years of eligibility remaining.