Per the California state Constitution, he seems to be, if he has been a resident there 5+ years:
CALIFORNIA CONSTITUTION
ARTICLE 5 EXECUTIVE
SEC. 2. The Governor shall be elected every fourth year at the same time and places as members of the Assembly and hold office from the Monday after January 1 following the election until a successor qualifies. The Governor shall be an elector who has been a citizen of the United States and a resident of this State for 5 years immediately preceding the Governor's election. The Governor may not hold other public office. No Governor may serve more than 2 terms.