Legendary entertainer Bob Hope and former U.S. President Bill Clinton ride away in their golf cart in this 1995 file photo at the Army-Navy Country Club in Arlington. (Stephen Jaffe/Reuters)

Arlington County has settled a tax dispute with its two privately owned golf courses, retroactively slashing their assessments and tax bills and promising to credit their overpayments from the last four years.

The settlement cuts the tax bill of the Army Navy Country Club from $1.56 million to $842,000 and drops the bill for the Washington Golf and Country Club to $460,000 from $872,400, county attorney Stephen MacIsaac said.

“We owe them a refund for the past four years,” during which the clubs paid taxes on the higher assessments, MacIsaac said. “Rather than cutting checks, we’re going to apply it to their future tax bills.”

The secretary-treasurer of Army Navy Country Club, Raighne Delaney, declined to comment. The general manager of the Washington Golf and Country Club, Patrick Tobey, did not return a phone call seeking comment. The settlement was first reported by the news site ­ARLnow.com.

The long-running dispute came to public attention this winter when the General Assembly passed a law ordering Arlington to cut the clubs’ tax rate from about $12 per square foot to 50 cents. The county fought the legislation, which the County Board said set “a dangerous precedent” because in Virginia, assessments are supposed to be under control of local governments. Gov. Ralph Northam (D) vetoed the bill, saying settlement negotiations were underway and the state should not interfere in a local dispute.

Under the agreement, the assessment for Army Navy was reduced from $149 million to $89.3 million, and the assessment for Washington Golf fell from $93 million to $47 million.

The zoning for both clubs, “large acreage parcels for residential use,” will not change under the agreement, MacIsaac said.

Advocates for the Arlington golf courses had said that they paid far more than other golf courses in Northern Virginia.

In the future, assessments for the courses will rise or drop based on the average percentage change in all residential assessments, according to the agreement.