In 2015, I filed as a California nonresident. So my foreign income was excluded. How do I do that this year as a California resident?
California should allow you to file as a Part-Year Resident. Any income you earned while you were not working in California (January 2016 - April 2016) will not be taxed in California. While you're filling out your State Taxes, you should get to a part under Adjustments called "Income Allocation to California". Here you can exclude your foreign income.