Rockefeller, 75, served for eight years as governor of the state before winning a Senate seat in 1984.
He was the first member of his family to run for public office as a Democrat.
"I'm going to serve out my term," Rockefeller said in an interview with Politico. "It was a very hard decision for me. Once it's made, like any hard decision, it eases up. But it was a very tough decision for me."
His decision means the seat will be up for grabs in 2014 with a Republican candidate having a good chance of winning it, the report said.
Rockefeller said fear of losing the next election was not a factor in his decision.
Rockefeller, great-grandson and namesake of oil baron John D. Rockefeller, moved to West Virginia in 1964 to work for the domestic equivalent of the Peace Corps. At the time, his uncle, Nelson Rockefeller, was the Republican governor of New York. Another uncle, Winthrop Rockefeller, was elected governor of Arkansas in 1966.
After losing a race for governor in 1972, Rockefeller won four years later.
Rockefeller told Politico one of his biggest mistakes was his 2003 vote in favor of the invasion of Iraq. His proudest achievements, he said, include the 1992 Coal Act, which provided health benefits for retired miners, and an expansion of Medicaid to cover more poor children.