Gov. Bob McDonnell is expected to tell lawmakers Thursday morning that Virginia has finished its fiscal year with a surplus of more than $360 million through higher-than-expected tax revenue and savings.

Last month, McDonnell (R) announced that the state had a surplus of $311 million on June 30, the close of the year, but since then he has said his administration has been able to save more than $50 million. He will release the total number Thursday.

Virginia law calls for the bulk of the money to be put into the state’s rainy day fund and spent on K-12 education, transportation and Chesapeake Bay cleanup.

McDonnell has proposed giving some of the unspent balance to sheriff’s offices across the state and to localities hit by recent tornadoes in southwest Virginia, as well as shoring up the pension system.

He will announce further recommendations for the money when he gives his annual speech on the state’s finances to the General Assembly’s money committees Thursday morning on Capitol Square.

Officials from counties and cities across the state have been lobbying McDonnell to restore $60 million in state aid to localities for fiscal year 2012 and the two-year budget he will unveil in December.

About 50 jurisdications have passed resolutions while nine Northern Virginia localities, including Fairfax County, sent a letter to McDonnell.

McDonnell spokesman Jeff Caldwell said much of the surplus money already has been allocated, but that the remainder will be considered during the next legislative session.

“The governor appreciates the hard decisions that have had to be made at the local level due to budget reductions and spending cuts in recent years as the nation and Virginia wrestle with the difficult economy,’’ Caldwell said. “The impacts of these cost-cutting measures have been felt at every level of government. However, it is through this type of sound fiscal management and belt tightening that the commonwealth has continued to live within its means and has mitigated the impacts of these difficult financial times on our citizens.”

The governor credited higher tax revenue - 5.8 percent growth in fiscal 2011, instead of a forecast 3.5 percent - as the main reason for the surplus.

A year ago, Virginia ended the fiscal year with a surplus of about $403.2 million - $229 million came from taxes, and the rest from savings.

Democrats criticized McDonnell for declaring a surplus after years of cuts to core services; delayed payments to the Virginia Retirement System; and a requirement that retailers pay sales tax a month early.

The General Assembly passed a $78 billion budget for fiscal 2011 and 2012 with no general tax increase. But the budget did include several fees and hundreds of millions of dollars in cuts, including to health care, schools and public safety, as it tried to close a $4 billion shortfall over the two years.