LOS ANGELES—California Gov. Jerry Brown appears poised to exit office next year with a top political priority in hand: free from the massive budget deficits that had weighed on his predecessors.

Buoyed by tax increases passed under his administration and a strong economy, Mr. Brown said Wednesday that the state is projecting a $6.1 billion surplus for the next fiscal year, which begins July 1.

The governor proposed socking most of the money away in a rainy-day fund whose creation he pushed for in 2014. Nearly 70% of the state’s projected revenue of about $135 billion next fiscal year is derived from personal income taxes, according to the governor’s office.

The state’s fiscal health is especially crucial as it faces myriad challenges: record natural disasters, housing shortages and changes to federal tax regulation—all while it ramps up opposition to the Trump administration on several major policy fronts.

As is his custom, the governor warned of an inevitable economic slowdown.