He made the announcement on MSNBC over the weekend.
A near-total abortion ban, based on a Civil War-era law from 1864 - before Arizona was even a state - is expected to go back into effect there within weeks.
Republicans in Arizona already passed a ban after 15 weeks of pregnancy.
Newsom's bill will be introduced this week through the California Legislature's women's caucus. It would essentially allow Arizona providers to be quickly licensed to treat their patients in California.