The Department of Energy yesterday won approval from the White House of a plan to clean up the nuclear wastes at a shutdown reprocessing plant near Buffalo, N.Y., in exchange for the state reopening a nearby burial ground for radioactive debris.

Under the plan, which must be submitted to Congress for approval, the Energy Department would remove the highly radioactive liquid waste from two tanks at the West Valley, N.Y., site, solidify the waste and then place it back in storage at the site until a permanent federal repository for nuclear waste is built somewhere in the United States.

While no financing of the cleanup has been agreed upon, it is understood the Energy Department will pay at least 70 percent of the bill. The cleanup is estimated to cost between $200 million and $300 million.

In addition to cleaning up the highlevel liquid wastes, the department will also take over the job of caring for the 400 tons of spent nuclear fuel stored in a huge pool of water at the West Valley site. The department plans to enlarge the storage pool to handle 600 tons more of spent fuel.

"The spent fuel will stay there but not permanently," said Worth Bateman, deputy director of the Office of Energy Research and the architect of the plan to clean up West Valley. "I'd say we'll be shipping spent fuel in there for the next 10 or 15 years, no more than that."

In return for the Energy Department's financing the cleanup, New York State has agreed to reopen the huge burial ground at West Valley where such things as radioactive clothing and medical containers are stored in steel drums. The burial site has been closed since 1972, ever since Nuclear Fuel Services Inc., shut down the reprocessing plant at West Valley.

The reopening of the West Valley burial site is seen as a necessity by the Energy Department, since the only burial ground east of the Mississippi River now licensed to take radioactive "bric-a-brac" is at Barnwell, S.C., and is fast filling up with steel drums. There were two other burial grounds in Kentucky and Illinois but both have been closed by the states in the last three years.

The land at West Valley is owned by New York State and leased to Nuclear Fuel Services, which is a subsidiary of Getty Oil Corp. The lease expires in 1980, at which time the closed plant and the radioactive waste go over to the state.