The High Line, a defunct railway that runs above Manhattan, is being transformed into a public park.

The media mogul Barry Diller and the fashion designer Diane Von Furstenberg have made a $10 million challenge grant to the High Line, the former elevated railway along the Hudson River that is being converted into a landscaped walkway. “I fell in love with the project, with the place,” Ms. Von Furstenberg said in a telephone interview. “It’s a beautiful green ribbon that will travel from Gansevoort to the Javits Center.”

The donation ranks among the four largest ever given by individuals to New York City parks, said the parks commissioner, Adrian Benepe. “There’s something about New York and parks that brings out extraordinary generosity,” he said.

After the donation was announced, another couple immediately volunteered to match it, Philip and Lisa Maria Falcone. That brings the fund-raising to $44 million in a $50 million capital campaign. It will be allotted in $2 million annual increments over five years, requiring Friends of the High Line, a nonprofit group that manages the project, to match each installment.

The first phase of the High Line, which runs from Gansevoort Street in the meatpacking district to 20th Street, is due to open some time this month. The meandering path 30 feet above the street — with plantings and water areas designed by Field Operations, a landscape architecture company, and Diller Scofidio & Renfro, the architectural firm — will ultimately extend all the way to 34th Street.

Under an operating agreement modeled on the Central Park Conservancy’s and signed last week, the Friends of the High Line will cover operating costs, which are expected to be $2 million to $4 million a year. The New York City Department of Parks and Recreation will provide security.

This marks the second major donation to the High Line from Mr. Diller and Ms. Von Furstenberg, who provided a $5 million gift in 2005. Both have offices near the High Line, Ms. Von Furstenberg on 14th Street and Mr. Diller’s IAC headquarters at 18th Street. “They were involved in supporting the High Line from the beginning,” said Joshua David, a co-founder of Friends of the High Line.

The total cost of the walkway’s first section is $86.2 million, Mr. David said, and the second phase — which extends to 30th Street — is expected to cost $66 million. The budget for the third section, which wraps around Hudson Yards, has yet to be determined.