A $20 million federal grant toward construction of high-occupancy toll lanes on Interstate 95 in Northern Virginia will help cement a tentative deal the state struck this month with a private contractor to build the $940 million project.

Fluor-Transurban, the company currently building toll lanes on Virginia’s portion of the Capital Beltway, has agreed to build 29 miles of HOT lanes between Edsall Road in Fairfax County and Garrisonville Road in Stafford County. The deal calls for Fluor-Transurban to foot $843 million of the cost, while the state contributes $97 million.

The federal help, which had been anticipated when the deal was negotiated, came as part of $511 million in grants announced by Transportation Secretary Ray LaHood under the TIGER (Transportation Investment Generating Economic Recovery) program. The money was awarded to 46 projects in 36 states in a competitive process that drew 828 applications. Neither Maryland nor the District received grants.

Virginia Transportation Secretary Sean T. Connaughton said that the state will use the grant to guarantee a loan of $150 million to $200 million under a federal program commonly known as TIFIA (Transportation Infrastructure Finance and Innovation Act). The program is used to leverage private capital for investment in transportation projects. In this case, Fluor-Transurban would be responsible for repayment of the loan, he said.

A critical change in the original project led transportation experts to question whether Fluor-Transurban can recover its investments while holding toll charges at a level drivers will be willing to pay.

Under the agreement, most existing lanes will remain toll-free. Vehicles carrying three or more people can use the toll lanes for free and others who opt to use them will pay tolls.

Until Arlington filed a lawsuit to block it , the plan called for the HOT lanes to continue north from Edsall Road until they reached the 14th Street Bridge into Washington. That final stretch is far more heavily traveled and would have been a cash cow to help support the rest of the project.

Construction could begin as early as next spring, Virginia officials said.

“I don’t think there’s a person in America who doesn’t know somebody who’s looking for work,” LaHood said, referring to the jobs the project will create.

The state’s two U.S. senators, James Webb (D) and Mark R. Warner (D), both welcomed the federal funding.

“The HOT lanes project will benefit commuters, enhance commerce and demonstrate how the government can partner with the private sector to address issues critical to our commonwealth,” Webb said.

Warner said the federal money would help leverage the private-sector investment.

“With the D.C. area ranked as the most congested in the country, this project is an important part of providing some relief and growing our economy,” Warner said.