The bill, passed by a 85-9 vote, also covers water transfers to help farmers in California and hundreds of water projects by the Army Corps of Engineers.
The House passed a similar bill two weeks ago. Once the measures are reconciled, the bill will go to the president for his signature.
The Yucca Mountain project, 90 miles from Las Vegas, was designed to hold 77,000 tons of waste but has been strongly opposed by the Nevada delegation.
The move fulfills Obama's campaign promise to close Yucca Mountain, which was 25 years and $13.5 billion in the making. It would, however, leave the country without a long-term solution for storing highly radioactive waste from nuclear power plants.
The 1987 law requiring waste to be stored at Yucca Mountain remains on the books, however, so the project could in theory be revived. The Yucca Mountain project would still receive the $196.8 million budgeted by Obama for work on the site, although the money wouldn't be used to ship waste there.
The Senate also adopted an amendment by California Democratic Sens. Dianne Feinstein and Barbara Boxer to allow water transfers to help California farmers suffering from severe drought conditions.
"I view this as a breakthrough in the water wars in California," Boxer said. "We were able to bring environmentalists together with the water districts."
The provision would facilitate transfer of water from the eastern portion of the San Joaquin Valley to the western part of the valley that has been particularly affected by a multiyear drought. Comparable language is in the House measure.