The new governor also said he would propose in his new budget, due out later this week, mandating that all Californians obtain health care insurance, in direct response to the Republican tax bill last year that removed the mandate from the Affordable Care Act. Such a mandate in California would require approval of the Legislature, which is far from assured.

His office also announced that he would create a surgeon general position for the state by executive order. His aides said the governor’s first budget would seek to expand Medi-Cal coverage to undocumented youths up to age 26.

Mr. Newsom, 51, had been the state’s lieutenant governor — largely a ceremonial position — for eight years under Mr. Brown. Before that, he served as mayor of San Francisco, where he positioned himself, for the most part, on the liberal side of the spectrum. He was an early promoter of same-sex marriage and the legalization of recreational marijuana.

On Monday, he used his speech to laud Mr. Brown’s tenure; the mention of his predecessor’s name drew a standing ovation. But Mr. Newsom left little doubt that he had a broader view of government than the moderate Mr. Brown. The departing governor inherited a $28 billion deficit and left Mr. Newsom a $14 billion surplus; he also created an $18 billion so-called rainy day fund to help the state get through what is widely viewed as an inevitable coming recession.

Mr. Brown’s insistence on holding onto state revenues was a source of continued friction with Democratic allies in the Legislature, who wanted to use the money to restore spending cuts that had been in place during the Great Recession.

Mr. Newsom’s agenda is likely to be costly, and thus likely to face obstacles as the new governor prepares to offer a new budget. Mr. Brown, among others, has warned that California is heading into a recession, and there are concerns in the business community and among some moderate Democrats that the former San Francisco mayor might take a decidedly different approach to spending than Mr. Brown.

Anthony Rendon, the Democratic speaker of the State Assembly, said in an interview Monday morning that while he supported some of Mr. Newsom’s initiatives, he had strong reservations about raising taxes to pay for them, as Mr. Newsom’s aides have suggested.