After philanthropist David M. Rubenstein agreed to fund half the cost of fixing the earthquake-damaged Washington Monument, he asked National Park Service Director Jonathan B. Jarvis: “What else you got?”

“Well, I have a long list,” Jarvis said he replied. At the top was the repair of the tattered 200-year-old Arlington House, which serves as the Robert E. Lee Memorial at Arlington National Cemetery. Its condition, Jarvis thought, was embarrassing.

Last winter, on a cold, rainy day, Jarvis gave Rubenstein a tour of the house where the famous Confederate general had lived before the Civil War. Rubenstein asked for a repair proposal.

“We proposed $12.3 million,” Jarvis said Thursday. He said Rubenstein replied, “Be glad to do that.”

On Thursday, Jarvis stood beside Rubenstein outside the portico of Arlington House and announced that the Bethesda billionaire is donating $12.35 million to rehabilitate the house, grounds and slave quarters.

The majestic Greek Revival home of Lee and his family for 30 years is one of the most beautiful spots in the area. The columned mansion sits high on a hill overlooking the cemetery, the Potomac River and the District.

The money is going to the National Park Foundation, the Park Service’s nonprofit fundraising partner. The Park Service operates Arlington House.

The donation will transform the site and the experience for the 650,000 people who visit each year, Park Service officials said. The house and grounds are to be restored to the way they were in 1860.

New interior lighting will be installed. Work will be done on the damaged foundation. And a state-of-the-art climate-control system will be installed.

Most of the work will happen in 2016. It will require the construction of scaffolding around the house and could require closing the museum and the slave quarters for nearly a year.

“My goal has been for the last couple years to give back to the country some of the good fortune that I’ve had,” Rubenstein said as he stood flanked by Jarvis and Neil Mulholland, president of the foundation.

“Some of that good fortune has been earned in Washington, D.C., and so I’m very interested in helping Washington, D.C., and the Washington area,” he said.

“When [the house is] repaired and restored, it’ll be more attractive for people to see and I think a better indication of what life was like here then,” he said later.

“The goal is to remind people of American history,” he said. “Unfortunately, people know so little about our history. . . . If you get a chance to tour this [house] and you think more about history . . . maybe you’ll be inspired to learn more about your country. And that’s really why I try to do this.”

Arlington House is rich in history. It is said to be modeled on the ancient Greek Temple of Hephaestus in Athens.

Built as a tribute to George Washington, it was also the place where, at the start of the Civil War, an anguished Lee decided to leave the U.S. Army and cast his lot with the South.

And over time, it became a centerpiece for the cemetery.

Rubenstein — co-founder of the Carlyle Group, a global private equity firm — has a passion for U.S. history and has made major history-themed donations in the past. He is especially interested in George Washington, and this is his third Washington-related donation.

His Washington Monument donation paid $7.5 million of the $15 million in the just-completed repairs required after the 2011 earthquake.

Last year, he paid $14.2 million for a rare copy of the 1640 Bay Psalm Book, said to be the first book printed in what became the United States. He said he planned to put the book on revolving loan to several libraries.

Earlier last year, he gave $10 million to Mount Vernon for a George Washington library.

The imposing Arlington mansion, with its eight columns and grand portico, was built mostly by the slaves of George Washington Parke Custis in three stages between 1802 and 1818.

Most of the house and its columns are made of brick covered with stucco made to look like stone. There is a massive century-old cedar tree in the back yard.

Custis, who had about 60 slaves at Arlington, was the step-grandson of George Washington. He had been raised by Washington at Mount Vernon and was devoted to the nation’s first president.

Custis built Arlington as a salute to Washington, and the home’s dining room still has dishware from Mount Vernon.

Custis’s daughter, Mary Anna, married Lee in the parlor of the home on June 30, 1831, and six of their seven children were born in the house, according to the Park Service.

“It is a noble-looking place, having a portico of stately white columns, which . . . with a background of dark woods, forms a beautiful object in the landscape,” the English novelist Francis M. Trollope wrote in 1832, according to a Park Service report.

Mary Anna Lee inherited the property when her father died in 1857, and her husband, then a highly regarded U.S. Army officer, took over its management and upkeep.

But with the outbreak of the Civil War, Lee resigned from the Army and left Arlington for Richmond on April 22, 1861. His wife left three weeks later.

The Union army quickly occupied the property because of its strategic location.

The cemetery, which is now run by the Army, was created three years later with the huge influx of dead soldiers from the bloody battles of 1864 and bitterness toward Lee over his role in the war.

The cemetery marked the 150th anniversary of its founding last month.

The Lees never lived in the mansion again, although in 1883, after a Supreme Court ruling, the government paid the family $150,000 for seizing the property, Matthew Penrod, a park ranger, said in a recent interview.

He said the settlement was finalized by Lee’s eldest son, Custis, and Abraham Lincoln’s eldest son, Robert, who was then the secretary of war.

In the years after the Civil War, the house went through cycles of decay and repair and for years was used as the home of the cemetery superintendent.

In 1925, Congress authorized restoration of the house, and it was designated a memorial to Lee. The National Park Service took over its management in 1933. The house has been on the National Register of Historic Places since 1966.