The decision means 1,100 employees will lose their jobs.
Beshear called the news disappointing and painful, even though he said it had been expected.
"We know there are 1,100 very talented and hardworking people at that facility, and we had hoped that an alternative might have been found to keep it open," the governor said. "As disheartening as this news is, we pledge our full assistance and support to the employees and community to absorb this loss and find new opportunities for those skilled and experienced workers."
The Cold War-era plant opened in 1952 to develop enriched uranium for military reactors and to produce nuclear weapons. The plant began selling uranium for commercial reactors in the 1960s, and it is now leased and operated by a private contractor, United States Enrichment Corp.
It stores 40,000 cylinders of depleted uranium.
The plant had been scheduled to close last year, but it got a reprieve under a temporary deal to enrich depleted uranium "tails" for Tennessee Valley Authority and Energy Northwest, a utility in Washington state.
Some employees had already received layoff notices.
"Paducah is a strong, resilient city full of dependable, creative people," Beshear said. "We are confident that those characteristics will carry citizens through this difficult time."
United States Enrichment Corp., which operates the Paducah plant, had applied to the federal government in February to keep the plant operating beyond May 31.
USEC leases the plant site from the DOE, which owns 3,556 acres on the property 15 miles west of Paducah.
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Related Story: USEC Contract Not Renewed, Plant to Begin Shutdown
